Calendar
Posted April 16, 2024
Last modified April 29, 2024
Faculty Meeting Questions or comments?
3:00 pm – 4:00 pm Lockett 232Meeting with Dean Cynthia Peterson
Posted April 19, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Peter Nelson, University of Waterloo
Infinite matroids on lattices
There are at least well-studied ways to extend matroids to more general objects - one can allow the ground set to be infinite, or instead define the concept of independence on a lattice other than a set lattice. I will discuss some nice ideas that arise when combining these two generalizations. This is joint work with Andrew Fulcher.
Posted January 16, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Jorge Poveda, University of California, San Diego
Donald P. Eckman, NSF CAREER, and AFOSR Young Investigator Program Awardee
Multi-Time Scale Hybrid Dynamical Systems for Model-Free Control and Optimization
Hybrid dynamical systems, which combine continuous-time and discrete-time dynamics, are prevalent in various engineering applications such as robotics, manufacturing systems, power grids, and transportation networks. Effectively analyzing and controlling these systems is crucial for developing autonomous and efficient engineering systems capable of real-time adaptation and self-optimization. This talk will delve into recent advancements in controlling and optimizing hybrid dynamical systems using multi-time scale techniques. These methods facilitate the systematic incorporation and analysis of both "exploration and exploitation" behaviors within complex control systems through singular perturbation and averaging theory, resulting in a range of provably stable and robust algorithms suitable for model-free control and optimization. Practical engineering system examples will be used to illustrate these theoretical tools.
Posted May 3, 2024
Last modified May 8, 2024
Probability Seminar Questions or comments?
11:00 am – 12:00 pm Zoom
Olga Iziumtseva, University of Nottingham
Asymptotic and geometric properties of Volterra Gaussian processes
In this talk we discuss asymptotic and geometric properties of Gaussian processes defined as $U(t) = \int_0^t K(t, s)dW(s),\ t \geq 0$, where $W$ is a Wiener process and $K$ is a continuous kernel. Such processes are called Volterra Gaussian processes. It forms an important class of stochastic processes with a wide range of applications in turbulence, cancer tumours, energy markets and epidemic models. Le Gall’s asymptotic expansion for the volume of Wiener Sausage shows that local times and self-intersection local times can be considered as the geometric characteristics of stochastic processes that look like a Wiener process. In this talk we discuss the law of the iterated logarithm, existence of local times and construct Rosen renormalized self-intersection local times for Volterra Gaussian processes.
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 1 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 2 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 3 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted April 29, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Giovanni Fusco, Università degli Studi di Padova
A Lie-Bracket-Based Notion of Stabilizing Feedback in Optimal Control
With reference to an optimal control problem where the state has to asymptotically approach a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a control Lyapunov function by a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree $k\ge 1$, and we call any of its (suitably defined) solutions a degree-k minimum restraint function. We prove that the existence of a degree-k minimum restraint function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost.
Posted June 4, 2024
Mathematical Physics and Representation Theory Seminar
3:30 pm – 4:30 pm Lockett 233
Mikhail Khovanov, Johns Hopkins University
Foams in algebraic K-theory and dynamics
We'll discuss a recent paper where algebraic K-theory is related to foams with a flat connection.
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Shea Vela-Vick, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Tristan Reynoso, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Megan Fairchild, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Shea Vela-Vick, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Colton Sandvik, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Tristan Reynoso, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Adithyan Pandikkadan, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Colton Sandvik, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Shea Vela-Vick, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Megan Fairchild, Louisiana State University
Classical Knot Concordance
Posted August 30, 2024
Last modified September 16, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233TBD
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Tristan Reynoso, Louisiana State University
Classical Knot Concordance
Posted June 12, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Nilangshu Bhattacharyya, Louisiana State University
Classical Knot Concordance
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Applied Mathematics
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Topology
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Analysis
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Algebra
Posted August 27, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233Organizational meeting
Posted August 21, 2024
Last modified August 28, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Rahul Kumar, Pennsylvania State University
Period function from Ramanujan's Lost Notebook and Kronecker limit formulas
The Lost Notebook of Ramanujan contains a number of beautiful formulas, one of which can be found on page 220. It involves an interesting function, which we denote as $\mathcal{F}_1(x)$. In this talk, we show that $\mathcal{F}_1(x)$ belongs to the category of period functions as it satisfies the period relations of Maass forms in the sense of Lewis and Zagier. Hence, we refer to $\mathcal{F}_1(x)$ as the Ramanujan period function. The Kronecker limit formulas are concerned with the constant term in the Laurent series expansion of certain Dirichlet series at $s=1$. We will also discuss that $\mathcal{F}_1(x)$ naturally appears in a Kronecker limit-type formula of a certain zeta function.
Posted August 30, 2024
Last modified September 3, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Huong Vo, Louisiana State University
Quasi-isometry and Milnor Schwarz theorem
In this talk, we will go over the proof of Milnor-Schwarz theorem, which states that a group G is quasi-isometric to a metric space X if it acts nicely on X. The definition of a quasi-isometry will be covered and so will other definitions relevant to the theorem.
Posted August 27, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Nilangshu Bhattacharyya, Louisiana State University
Transverse invariant as Khovanov skein spectrum at its extreme Alexander grading
Olga Plamenevskaya described a transverse link invariant as an element of Khovanov homology. Lawrence Roberts gave a link surgery spectral sequence whose $E^2$ page is the reduced Khovanov skein homology (with $\mathbb{Z}_{2}$ coefficient) of a closed braid $L$ with odd number of strands and $E^{\infty}$ page is the knot Floer homology of the lift of the braid axis in the double branch cover, and the spectral sequence splits with respect to the Alexander grading. The transverse invariant does not vanish in the Khovanov skein homology, and under the above spectral sequence and upon mapping the knot Floer homology to the Heegard Floer homology, the transverse invariant corresponds to the contact invariant. Lipshitz-Sarkar gave a stable homotopy type invariant of links in $S^3$. Subsequently, Lipshitz-Ng-Sarkar found a cohomotopy element in the Khovanov spectrum associated to the Plamenevskaya invariant. We can think of this element as a map from Khovanov spectra at its extreme quantum grading to the sphere spectrum. We gave a stable homotopy type for Khovanov skein homology and showed that we can think of the cohomotopy transverse element as a map from the Khovanov spectra at its extreme quantum grading to the Khovanov skein spectra at its extreme Alexander grading. This is a joint work with Adithyan Pandikkadan, which will be presented in this talk.
Posted August 31, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Ugo Boscain, Sorbonne University, France
3D Optimal Control Problems Constrained on Surfaces
In this talk I consider a surface embedded in a 3D contact sub-Riemannian manifold (i.e., an optimal control problem in dimension 3 with 2 controls which is linear with respect to the controls and with quadratic cost; we will also make a natural controllability assumption). Such a surface inherits a field of direction (with norm) from the ambient space. This field of directions is singular at characteristic points (i.e., where the surface is tangent to the set of admissible directions). In this talk we will study when the problem restricted to the surface is controllable, in other words when the normed field of directions permits to give to the surface the structure of metric space (of SNCF type). We will also study how to define the heat and the Schroedinger equation on such a structure and if the singular points are “accessible” or not by the evolution.
Posted August 28, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett Hall 233 (Simulcasted via Zoom)
Yiwei Ge, Louisiana State University
Reconstructing induced-$C_4$-free graphs from digitally convex sets
A set $S$ of vertices is {\it digitally convex} if for every vertex $v$, $N[v]\subseteq N[S]$ implies $v\in S$. In 2014, Lafrance, Oellermann, and Pressey showed that trees are reconstructable from their digitally convex sets. We improved upon that result by showing that all induced-$C_4$-free graphs are reconstructable from their digitally convex sets, and we provide an algorithm for the reconstruction. This is based on a project with a group from the Graduate Research Workshop in Combinatorics (GRWC).
Posted August 14, 2024
Last modified September 5, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Heidi Goodson, Brooklyn College, CUNY
An Exploration of Sato-Tate Groups of Curves
The focus of this talk is on families of curves and their associated Sato-Tate groups -- compact groups predicted to determine the limiting distributions of coefficients of the normalized L-polynomials of the curves. Complete classifications of Sato-Tate groups for abelian varieties in low dimension have been given in recent years, but there are obstacles to providing classifications in higher dimension. In this talk I will give an overview of the techniques we can use for some nice families of curves and discuss the ways in which these techniques fall apart when there are degeneracies in the algebraic structure of the associated Jacobian varieties. I will include examples throughout the talk in order to make the results more concrete to those new to this area of research.
Posted September 10, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom Link
Anton Dochtermann, Texas State University
Cycle systems, parking functions, and h-vectors of matroids
The h-vector of a matroid M is an important invariant related to the independence complex of M, which can also be covered as an evaluation of its Tutte polynomial. A well-known conjecture of Stanley posits that the h-vector of a matroid is a "pure O-sequence", meaning that it can be recovered by counting faces of a pure multicomplex. Merino has established Stanley's conjecture for the case of cographic matroids via a connection to chip-firing on graphs and the concept of a G-parking function. Inspired by these constructions, we introduce the notion of a cycle system for a matroid M . This leads to a collection of integer sequences that we call (co)parking functions for M, which we show are in bijection with the set of bases of M. We study maximal coparking functions, and also how cycle systems behave under deletion and contraction. This leads to a proof of Stanley’s conjecture for the case of matroids that admit cycle systems. This is joint work with Scott Cory, Solis McClain, and David Perkinson.
Posted August 30, 2024
Last modified September 16, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Saumya Jain, Louisiana State University
Quasi-isometric invariance of hyperbolicity
In this talk, we will define $\delta$-hyperbolic spaces and show that geodesics and quasi-geodesics stay close in a hyperbolic space. We will then prove that hyperbolicity is a quasi-isometric invariant.
Posted August 28, 2024
Last modified September 9, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Tristan Wells Filbert, Louisiana State University
Whitehead doubles of dual knots are deeply slice
In collaboration with McConkey, St. Clair, and Zhang, we show that the Whitehead double of the dual knot to $1/n$ surgery on the knot $6_1$ in the 3-sphere is deeply slice in a contractible 4-manifold. That is, it bounds a smoothly embedded disc in the manifold, but not in a collar neighborhood of its boundary, the surgered manifold. This is partial progress in answering one of the Kirby questions regarding nullhomotopic deeply slice knots, mentioned in earlier work of Klug and Ruppik. To prove our theorem, we make use of the immersed curves perspective of bordered Floer homology and knot Floer homology.
Posted September 3, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Denis Efimov, University of Lille
Homogeneity with Respect to a Part of Variables and Accelerated Stabilization
The presentation addresses the problem of transforming a locally asymptotically stabilizing time-varying control law to a global one with accelerated finite/fixed-time convergence rates. The approach relies on an extension of the theory of homogeneous systems to homogeneity only with respect to a part of the state variables and on the associated partial stability properties. The proposed control design builds upon the kind of approaches first studied in [MCloskey and Murray,1997] and uses the implicit Lyapunov function framework. A sampled-time implementation scheme of the control law is also presented and its properties are characterized. The method is illustrated by finite-time and nearly fixed-time stabilization of a nonholonomic integrator.
Posted September 13, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Friday, September 13, 2024 Zoom Link
Bryce Frederickson, Emory
Turán and Ramsey problems in vector spaces over finite fields
Abstract: Turán-type problems ask for the densest-possible structure which avoids a fixed substructure H. Ramsey-type problems ask for the largest possible "complete" structure which can be decomposed into a fixed number of H-free parts. We discuss some of these problems in the context of vector spaces over finite fields. In the Turán setting, Furstenberg and Katznelson showed that any constant-density subset of the affine space $AG(n,q)$ must contain a $k$-dimensional affine subspace if n is large enough. On the Ramsey side of things, a classical result of Graham, Leeb, and Rothschild implies that any red-blue coloring of the projective space $PG(n-1,q)$ must contain a monochromatic k-dimensional projective subspace, for n large. We highlight the connection between these results and show how to obtain new bounds in the latter (projective Ramsey) problem from bounds in the former (affine Turán) problem. This is joint work with Liana Yepremyan.
Posted September 19, 2024
5:30 pm James E. Keisler Lounge (room 321 Lockett)Actuarial Student Association Meeting
We will have a guest visitor Aimee Milam from CareSource. Pizza will be served.
Posted August 30, 2024
Last modified September 23, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Rachel Meyers, Louisiana State University
Quasi-isometries and Boundaries of $\delta$-Hyperbolic Spaces
In this talk, we define the boundary of a $\delta$-hyperbolic space as a set of rays and describe the topology of X with this boundary. Further, we will prove if two spaces are quasi-isometric then the boundaries are homeomorphic.
Posted September 15, 2024
7:50 am – 2:00 pm Virtually via Zoom, Click here to join Zoom, Meeting ID: 894 8105 1822, Passcode: SIIT-LSU24SIIT-LSU Conference on Analysis and PDE In Honor of Igor E. Verbitsky’s Retirement
This is an Analysis and PDE international joint conference between LSU and Sirindhorn International Institute of Technology (SIIT), Thailand, in honor of Professor Igor E. Verbitsky’s Retirement. The conference will take place virtually via Zoom and everyone is invited to participate. All the conference materials are now available on the conference website: https://sites.google.com/view/siit-lsu/
Posted August 27, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Jean Auriol, CNRS Researcher, L2S, CentraleSupélec
Robust Stabilization of Networks of Hyperbolic Systems with Chain Structure
In this talk, we focus on recent developments for the stabilization of networks of elementary hyperbolic systems with a chain structure. Such a structure arises in multiple industrial processes such as electric power transmission systems, traffic networks, or torsional vibrations in drilling devices. The objective is to design feedback control laws that stabilize the chain using the available actuators and sensors. The different systems composing the network are called elementary in the sense that when taken alone, we know how to design stabilizing output-feedback control laws. We will first consider the case where the actuators and sensors are available at one end of the chain. Using appropriate state predictors, we will present a recursive approach to stabilize the whole chain. Then, we will focus on the case where the actuators and sensors are only available at the junction between two subsystems composing the chain. We will show that such a configuration does not always guarantee the controllability of the chain. Under appropriate controllability/observability conditions, we will design simple stabilizing control laws. Our approach will be based on rewriting the system as Integral Delay Equations (IDEs) with pointwise and distributed control terms. Finally, we will show how the proposed techniques can be used to develop output feedback control laws for traffic flow on two cascaded freeway segments connected by a junction.
Posted September 21, 2024
LSU AWM Student Chapter LSU AWM Student Chapter Website
12:00 pm – 1:00 pm Keisler Lounge, Lockett HallAssociation of Women in Mathematics- Student chapter- Lunch and INFO SESSION
Join us to discuss upcoming events and opportunities to get involved in LSU’s Association for Women in Mathematics. Refreshments will be provided! Hope to see you there!
Posted September 19, 2024
1:30 pm – 2:30 pm Keisler LoungeMeet & Greet with Jon Loftin (MathWorks)
Pizza will be served. Jon Loftin will present on "Deep Learning with MATLAB: A Visual Approach" after the lunch.
Posted September 17, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom Link
Matthew Kroeker, Waterloo
Unavoidable flats in matroids representable over a finite field
For a positive integer k and finite field F, we prove that every simple F-representable matroid with sufficiently high rank has a rank-k flat which either is independent, or is a projective or affine geometry over a subfield of F. As a corollary, we obtain the following Ramsey theorem: given an F-representable matroid of sufficiently high rank and any 2-colouring of its points, there is a monochromatic rank-k flat. This is joint work with Jim Geelen and Peter Nelson.
Posted September 19, 2024
2:30 pm – 3:30 pm Lockett 284Deep Learning with MATLAB: A Visual Approach
Deep learning is quickly becoming embedded in everyday applications. It’s becoming essential for students and educators to adopt this technology to solve complex real-world problems. MATLAB and Simulink provide a flexible and powerful platform to develop and automate data analysis, deep learning, AI, and simulation workflows in a wide range of domains and industries. In this workshop we will introduce deep learning with MATLAB. We will utilize a previously trained network and modify it, using the MATLAB Deep Network Designer. The Deep Network Designer allows you to interactively build, visualize, and train neural networks. Individuals can generate the code for the neural network and finetune parameters. Users can use popular pre-trained networks or construct their own. We will also look at the MATLAB Classification Learner to run several models on a single data set. These visual approaches create a more efficient workflow.
Posted August 30, 2024
Last modified September 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Nilangshu Bhattacharyya, Louisiana State University
Some basic hyperbolic geometry
We will first discuss hyperboloid model for hyperbolic space and then discuss ball model and upper half space model. Furthermore, we will define the boundary at infinity and implicitly identify with spheres. We move on to talk about isometry group of hyperbolic spaces and classifying them (elliptic, parabolic and hyperbolic), with some examples. If time permits, I may state the Mostow's rigidity theorem.
Posted September 18, 2024
Last modified January 7, 2025
Ian Tobasco, Rutgers University
Rigidity and Elasticity
This talk will introduce elasticity theory from the geometric point of view for students from mathematics and related disciplines. Our basic objects of study will be (nearly) length preserving maps that arise from (nearly) minimizing an energy functional having to do with the amount of work required to deform a body. After defining the basic quantities of interest, we will discuss Fritz John's seminal study of small strain maps, along with his counterexample to rigidity and its ultimate resolution in the early 2000s by Friesecke, James, and Müller. Time permitting, we will discuss a bit about elastic patterns --- fine structures that occur in naturally wrinkled or crumpled sheets that show us what we do not yet understand about the rigidity of thin elastic domains.
Posted September 27, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 381
Padmanabhan Sundar, Mathematics Department, LSU
Uniqueness and stability for the Boltzmann-Enskog equation
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann–Enskog equation. By the introduction of a shifted distance, an inequality is proven on the Wasserstein distance for any two measure-valued solutions to the Boltzmann–Enskog equation. Using it, we find sufficient conditions for the uniqueness and continuous-dependence on initial data for solutions of the equation. This is a joint work with Martin Friesen and Barbara Ruediger.
Posted July 13, 2024
Last modified September 16, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Ian Tobasco, Rutgers University
Homogenization of Kirigami and Origami-Based Mechanical Metamaterials
Mechanical metamaterials are many-body elastic systems that deform in unusual ways, due to the interactions of nearly rigid building blocks. Examples include origami patterns with many folds, or kirigami patterns made by cutting material from an elastic sheet. In either case, the local deformations of the pattern involve internal degrees of freedom which must be matched with the usual global Euclidean invariances --- e.g., groups of origami panels move by rotations and translations while the whole pattern bends into a curved shape. This talk will introduce the homogenization problem for kirigami and origami metamaterials to a broad audience, and describe our recent results. Our goal is to explain the link between the design of the individual cuts/folds and the bulk deformations they produce. This is joint work with Paul Plucinsky (U. Southern California, Aerospace and Mechanical Engineering) and Paolo Celli (Stony Brook U., Civil Engineering). This talk will be mathematically self-contained, not assuming a background in elasticity.
Posted August 11, 2024
Last modified September 22, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Panagiotis Tsiotras, Georgia Institute of Technology
AIAA and IEEE Fellow
From Covariance Control to Covariance Steering: The First 40 Years
Uncertainty propagation and mitigation is at the core of all robotic and control systems. The standard approach so far has followed the spirit of control of a system “with uncertainties,” as opposed to the direct control “of uncertainties.” Covariance control, developed by Bob Skelton and his colleagues in the early 80’s, was introduced as a principled approach to handle uncertainty with guarantees in the asymptotic case. The finite-time case has only been recently addressed, and borrowing ideas from the classical optimal mass transport and the Schrödinger Bridge problems, provides a new tool to control stochastic systems with strict performance guarantees that go beyond classical controllability results that only hold for deterministic systems. In this talk, I will review recent results on covariance and distribution control for discrete stochastic systems, subject to probabilistic (chance) constraints, and will demonstrate the application of the approach on control and robot motion planning problems under uncertainty. I will also discuss current trends and potential directions for future work.
Posted August 28, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Ce Chen, University of Illinois Urbana-Champaign
On the maximum $F$-free induced subgraphs in $K_t$-free graphs
For graphs $F$ and $H$, let $f_{F,H}(n)$ be the minimum possible size of a maximum $F$-free induced subgraph in an $n$-vertex $H$-free graph, which is a generalization of both the Ramsey function and the Erd\H{o}s--Rogers function. Assuming the existence of certain locally dense $H$-free graphs, we give a general upper bound on $f_{F,H}(n)$ by establishing a container lemma for the $F$-free subgraphs. In particular, we improve the upper bounds on $f_{F,H}(n)$ when H is $K_3$ and $K_4$. This is joint work with J\'{o}zsef Balogh and Haoran Luo.
Posted September 27, 2024
Last modified October 1, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Tom Gannon, UCLA
Quantization of the universal centralizer and central D-modules
We will discuss joint work with Victor Ginzburg that proves a conjecture of Nadler on the existence of a quantization, or non-commutative deformation, of the Knop-Ngô morphism—a morphism of group schemes used in particular by Ngô in his proof of the fundamental lemma in the Langlands program. We will first explain the representation-theoretic background, give an extended example of this morphism for the group GL_n(C), and then present a precise statement of our theorem. Time permitting, we will also discuss how the tools used to construct this quantization can also be used to prove conjectures of Ben-Zvi and Gunningham, which predict a relationship between the quantization of the Knop-Ngô morphism and the parabolic induction functor.
Posted October 4, 2024
5:30 pm James E. Keisler Lounge (room 321 Lockett)Actuarial Student Association Meeting
We will have guest speaker Morgan Ascanio from Symetra. We will also vote on bylaws for the club. Pizza will be served.
Posted August 21, 2024
Last modified October 7, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Wanlin Li, Washington University in St. Louis
Non-vanishing of Ceresa and Gross–Kudla–Schoen cycles
The Ceresa cycle and the Gross–Kudla–Schoen modified diagonal cycle are algebraic $1$-cycles associated to a smooth algebraic curve with a chosen base point. They are algebraically trivial for a hyperelliptic curve and non-trivial for a very general complex curve of genus $\ge 3$. Given a pointed algebraic curve, there is no general method to determine whether the Ceresa and GKS cycles associated to it are rationally or algebraically trivial. In this talk, I will discuss some methods and tools to study this problem.
Posted October 3, 2024
Faculty Meeting Questions or comments?
1:30 pm – 2:30 pm ZoomFaculty Meeting with the Dean
Posted August 30, 2024
Last modified October 7, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Krishnendu Kar, Louisiana State University
Goodwillie-ingly Exploring Taylor Towers: Unravelling Functor Calculus
The study of the calculus of a function is the study of local behaviour of the function. One of the biggest features of calculus is approximation, i.e. given an unknown function; we may approximate to known functions to tell its property. A key example is Taylor series approximation, for a $n$ times differentiable function we can approximate to a polynomial of degree $n$. Goodwillie unlocked these deceptively simple yet so useful features of functions for functors, mostly to study K-theories. We may approximate a functor by suitable polynomial functors, and analogously, we get something called a Taylor tower. A key question here is how one might define the derivative of a functor in such a way it is commensurate with the original theory of calculus. Then, given a Taylor tower, we ask similar questions as we ask a Taylor series, how does Taylor tower converge in some analogous way? In this talk, we will explore some notions of Goodwillie’s calculus and answer some of the questions imposed.
Posted July 11, 2024
Faculty Meeting Questions or comments?
3:30 pm – 4:30 pm tbaCollege of Science Fall Convocation
Posted October 8, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Karl Worthmann, Institute of Mathematics, Technische Universität Ilmenau
Koopman-Based Control with Guarantees
Extended dynamic mode decomposition (EDMD), embedded in the Koopman framework, is a widely-applied technique to predict the evolution of an observable along the flow of a dynamical control system. However, despite its popularity, the error analysis is still fragmentary. We provide a complete and rigorous analysis for control-affine systems by splitting up the approximation error into the projection and estimation error resulting from the finite dictionary size and the finite amount of i.i.d. data used to generate the surrogate model. Further, we indicate extensions towards reproducible kernel Hilbert spaces to establish L∞-error bounds using kernel EDMD. Then, we demonstrate the applicability of the EDMD surrogate models for the control of nonlinear systems.
Posted October 4, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett Hall 233 (simulcasted via Zoom)
Zilin Jiang, Arizona State University
Beyond the classification theorem of Cameron, Goethals, Seidel, and Shult
The classification of graphs with smallest eigenvalues at least −2 culminated in a beautiful theorem of Cameron, Goethals, Seidel and Shult, who related such graphs to root systems from the representation theory of semisimple Lie algebras. In this talk, I will explore graphs with smallest eigenvalues between −2 and −λ*, where λ* is about 2.0198, and I will explain why the mysterious number λ* is a barrier for classification. Joint work with Alexander Polyanskii and Hricha Acharya.
Posted October 9, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Tobias Simon, University of Erlangen, Germany
Realizations of irreducible unitary representations of the Lorentz group in spaces of distributional sections over de Sitter space
In Algebraic Quantum Field Theory, one is interested in constructing nets of local von Neumann algebras satisfying the Haag Kastler axioms. Every such net defines a local net of standard subspaces in the corresponding Hilbert space by letting the selfadjoint elements in the local algebras act on a common cyclic and separating vector. In this talk, we discuss work by Frahm, Neeb and Olafsson which constructs nets standard subspaces on de Sitter space satisfying the corresponding axioms. Here the main tool is "realizing" irreducible unitary representations of the Lorentz group SO(1,d) in spaces of distributional sections over de Sitter space. These can be constructed from SO(1,d-1)-finite distribution vectors obtained as distributional boundary values of holomorphically extended orbit maps of SO(d)-finite vectors. Our main contribution is the proof of polynomial growth rates of these orbit maps, which guarantees the existence of the boundary values in the space of distribution vectors.
Posted October 9, 2024
11:00 am – 12:00 pm TBD"What to do in Summer"
Join us for the "Summer Opportunities Event," organized by the SIAM Student Chapter! This session will provide valuable insights on building effective CVs and resumes, as well as exploring a variety of summer opportunities such as internships, summer schools, and workshops. The event will help you enhance your academic profile, gain professional experience, and guide you in finding the right opportunities and preparing the necessary materials.
Posted October 14, 2024
Faculty Meeting Questions or comments?
3:00 pm – 3:45 pm Thursday, October 10, 2024 ZoomMeeting of the Tenured Faculty
Posted August 30, 2024
Last modified October 17, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Adithyan Pandikkadan, Louisiana State University
Construction of Hyperbolic Manifolds
In this talk, we will discuss two ways for constructing hyperbolic manifolds. We will begin by introducing hyperbolic surfaces, focusing on how to equip a hyperbolic structure on higher genus surfaces. Following this, we will discuss the construction of arithmetic hyperbolic manifolds which is a more general approach.
Posted October 14, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 381
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted August 29, 2024
Last modified October 7, 2024
Geometry and Topology Seminar Seminar website
3:30 pm
Bin Sun, Michigan State University
$L^2$-Betti numbers of Dehn fillings
I will talk about a recent joint work with Nansen Petrosyan where we obtain conditions under which $L^2$-Betti numbers are preserved by group-theoretic Dehn fillings. As an application, we verify the Singer Conjecture for certain Einstein manifolds and provide new examples of hyperbolic groups with exotic subgroups. We also establish a virtual fibering criterion and obtain bounds on deficiency of Dehn fillings. A key step in our approach of computations of $L^2$-Betti numbers is the construction of a tailored classifying space, which is of independent interest.
Posted September 27, 2024
Last modified October 16, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Xinchun Ma, University of Chicago
Cherednik algebras, Torus knots and flag commuting varieties
In this talk, we will explore how the Khovanov-Rozansky homology of the (m,n)-torus knot can be extracted from the finite-dimensional representation of the rational Cherednik algebra at slope m/n, equipped with the Hodge filtration. Our approach involves constructing a family of coherent sheaves on the Hilbert scheme of points on the plane, arising from cuspidal character D-modules. In describing this family of coherent sheaves, the geometry of nilpotent flag commuting varieties naturally emerges, closely related to the compactified regular centralizer in type A.
Posted October 4, 2024
5:30 pm James E. Keisler Lounge (room 321 Lockett)Actuarial Student Association Meeting
We will have guest speaker Jordan Hayes from AETNA (CVS Health). Pizza will be served.
Posted August 14, 2024
Last modified October 17, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm Lockett 233 or click here to attend on Zoom
Brian Grove, LSU
The Explicit Hypergeometric Modularity Method
The existence of hypergeometric motives predicts that hypergeometric Galois representations are modular. More precisely, explicit identities between special values of hypergeometric character sums and coefficients of certain modular forms on appropriate arithmetic progressions of primes are expected. A few such identities have been established in the literature using various ad-hoc techniques. I will discuss a general method to prove these hypergeometric modularity results in dimensions two and three. This is joint work with Michael Allen, Ling Long, and Fang-Ting Tu.
Posted October 18, 2024
Computational Mathematics Seminar
3:30 pm DMC 1034
Xili Wang, Peking University
DL for PDEs: towards parametric, high-dimensional and PDE-constrained optimization
Despite advances in simulating multiphysics problems through numerical discretization of PDEs, mesh-based approximation remains challenging, especially for high-dimensional problems governed by parameterized PDEs. Moreover, other PDE-related problems, such as PDE-constrained shape optimization, introduce additional difficulties including mesh deformation and correction. While Physics-Informed Neural Networks (PINNs) offer an alternative, they often lack the accuracy of traditional methods like finite element methods. Relying solely on a 'black-box' approach may not be the best choice for scientific computing. Inspired by adaptive finite element methods, we propose a deep adaptive sampling approach to solve low-regularity parametric PDEs and high-dimensional committor functions in rare event simulations. Additionally, by integrating the mesh-free nature of neural networks into the direct-adjoint looping (DAL), we achieve fully mesh-independent solutions for PDE-constrained shape optimization problems.
Posted August 30, 2024
Last modified October 17, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Megan Fairchild, Louisiana State University
Slicing Obstructions from 4-Manifold Theory
The orientable 4 genus of a knot is defined to be the minimum genus amongst all smoothly embedded surfaces in the 4-ball with boundary the knot. A knot is called slice if it bounds a smoothly embedded disk in the 4-ball. Invariants of knots, either classical or Heegaard Floer, are commonly used as lower bounds for the orientable 4 genus of knots. We will examine a different approach to showing knots are not smoothly slice, coming from 4-manifold theory.
Posted October 22, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 237
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 2
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted October 15, 2024
Last modified October 22, 2024
Nathan Mehlhop, Louisiana State University
Ergodic averaging operators
Certain quantitative estimates such as oscillation inequalities are often used in the study of pointwise convergence problems. Here, we study these for discrete ergodic averaging operators and discrete singular integrals along polynomial orbits in multidimensional subsets of integers or primes. Because of its relevance to multiparameter averaging operators, we also consider the vector-valued setting. Several tools including the Hardy-Littlewood circle method, Weyl's inequality, the Ionescu-Wainger multiplier theorem, the Magyar-Stein-Wainger sampling principle, the Marcinciewicz-Zygmund inequality, and others, are important in this field. The talk will introduce the problem and many of these ideas, and then give some outline of how the various estimates can be put together to give the conclusion.
Posted August 19, 2024
Last modified September 27, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Andrii Mironchenko, University of Klagenfurt
IEEE CSS George S. Axelby Outstanding Paper Awardee
Superposition Theorems for Input-to-State Stability of Time-Delay Systems
We characterize input-to-state stability (ISS) for nonlinear time-delay systems (TDS) in terms of stability and attractivity properties for systems with inputs. Using the specific structure of TDS, we obtain much tighter results than those possible for general infinite-dimensional systems. The subtle difference between forward completeness and boundedness of reachability sets (BRS) is essential for the understanding of the ISS characterizations. As BRS is important in numerous other contexts, we discuss this topic in detail as well. We shed light on the differences between the ISS theories for TDS, generic infinite-dimensional systems, and ODEs.
Posted October 1, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Friday, October 4, 2024 Zoom Link
Andrew Fulcher, University College Dublin
The cyclic flats of L-polymatroids
In recent years, $q$-polymatroids have drawn interest because of their connection with rank-metric codes. For a special class of $q$-polymatroids called $q$-matroids, the fundamental notion of a cyclic flat has been developed as a way to identify the key structural features of a $q$-matroid. In this talk, we will see a generalization of the definition of a cyclic flat that can apply to $q$-polymatroids, as well as a further generalization, $L$-polymatroids. The cyclic flats of an $L$-polymatroid is essentially a reduction of the data of an $L$-polymatroid such that the $L$-polymatroid can be retrieved from its cyclic flats. As such, in matroid theory, cyclic flats have been used to characterize numerous invariants.
Posted September 25, 2024
Last modified October 7, 2024
(Originally scheduled for Tuesday, October 8, 2024)
Summer Opportunities
TBA DATE is still to be determined!
Posted September 27, 2024
Last modified October 24, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Nikolay Grantcharov, University of Chicago
Infinitesimal structure of BunG
Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on the Fulton-Macpherson compactification of the configuration space, with logarithmic singularities along the diagonal divisor. We also briefly discuss applications into constructing Hitchin's flat connection on the vector bundle of conformal blocks.
Posted September 26, 2024
Last modified October 25, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Matias Delgadino, University of Texas at Austin
Generative Adversarial Networks: Dynamics
Generative Adversarial Networks (GANs) was one of the first Machine Learning algorithms to be able to generate remarkably realistic synthetic images. In this presentation, we delve into the mechanics of the GAN algorithm and its profound relationship with optimal transport theory. Through a detailed exploration, we illuminate how GAN approximates a system of PDE, particularly evident in shallow network architectures. Furthermore, we investigate known pathological behaviors such as mode collapse and failure to converge, and elucidate their connections to the underlying PDE framework through an illustrative example.
Posted August 21, 2024
Last modified October 25, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Brett Tangedal, University of North Carolina, Greensboro
Real Quadratic Fields and Partial Zeta-Functions
We focus on real quadratic number fields and explain an approach to the partial zeta-functions associated with the various ideal class groups of such fields dating back to the original work of Zagier, Stark, Shintani, David Hayes, and others. Along the way, we will give a brief introduction to Stark's famous first order zero conjecture.
Posted August 30, 2024
Last modified October 27, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Matthew Lemoine, Louisiana State University
A Brief Introduction to Khovanov Homology through an example
In this talk, we will discuss Khovanov Homology and how to compute this homology using an example with the trefoil knot. We will also discuss the relations between Khovanov Homology and the Jones Polynomial.
Posted October 7, 2024
Last modified October 28, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Monika Kudlinska, University of Cambridge
Solving equations in free-by-cyclic groups
A group G is said to be free-by-cyclic if it maps onto the infinite cyclic group with free kernel of finite rank. Free-by-cyclic groups form a large and widely-studied class with close links to 3-manifold topology. A group G is said to be equationally Noetherian if any system of equations over G is equivalent to a finite subsystem. In joint work with Motiejus Valiunas we show that all free-by-cyclic groups are equationally Noetherian. As an application, we deduce that the set of exponential growth rates of a free-by-cyclic group is well ordered.
Posted October 29, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 237
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 3
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted August 26, 2024
Last modified October 24, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Angelia Nedich, Arizona State University
Resilient Distributed Optimization for Cyber-physical Systems
This talk considers the problem of resilient distributed multi-agent optimization for cyber-physical systems in the presence of malicious or non-cooperative agents. It is assumed that stochastic values of trust between agents are available which allows agents to learn their trustworthy neighbors simultaneously with performing updates to minimize their own local objective functions. The development of this trustworthy computational model combines the tools from statistical learning and distributed consensus-based optimization. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: 1) almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network, 2) the deviation of the converged limit, from the nominal no attack case, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially, and 3) correct classification of malicious and legitimate agents can be attained in finite time almost surely. Further, the expected convergence rate decays exponentially with the quality of the trust observations between agents. We then combine this trust-learning model within a distributed gradient-based method for solving a multi-agent optimization problem and characterize its performance.
Posted October 29, 2024
LSU AWM Student Chapter LSU AWM Student Chapter Website
12:30 pm – 1:20 pmAWM Student Chapter Q & A Session with Prof. Angelia Nedich
Join us for a QA session hosted by the Association for Women in Mathematics (AWM) Student Chapter. We are honored to have Prof. Angelia Nedich from Arizona State University, a leading convex analysis and optimization researcher. Prof. Nedich will share insights from her research and discuss her academic experiences.
Posted November 1, 2024
5:30 pm James E. Keisler Lounge (room 321 Lockett)Actuarial Student Association Meeting
Guest speaker Jack Berry from Cigna health will speak. Pizza will be served.
Posted October 8, 2024
Last modified October 30, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Virtual talk: click here to attend on Zoom
Linli Shi, University of Connecticut
On higher regulators of Picard modular surfaces
The Birch and Swinnerton-Dyer conjecture relates the leading coefficient of the L-function of an elliptic curve at its central critical point to global arithmetic invariants of the elliptic curve. Beilinson’s conjectures generalize the BSD conjecture to formulas for values of motivic L-functions at non-critical points. In this talk, I will relate motivic cohomology classes, with non-trivial coefficients, of Picard modular surfaces to a non-critical value of the motivic L-function of certain automorphic representations of the group GU(2,1).
Posted August 30, 2024
Last modified November 4, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Nilangshu Bhattacharyya, Louisiana State University
Gromov norm of a compact manifold and straightening
We will define the Gromov norm of a compact manifold and straightening (every singular chain is naturally homotopic to a straight one).
Posted October 12, 2024
Last modified October 30, 2024
Vishwa Dewage, Clemson University
The Laplacian of an operator and applications to Toeplitz operators
Werner's quantum harmonic analysis (QHA) provides a set of tools that are applicable in many areas of analysis, including operator theory. As noted by Fulsche, QHA is particularly suitable to study Toeplitz operators on the Fock space. We explore the Laplacian of an operator and a heat equation for operators on the Fock space using QHA. Then we discuss some applications to Toeplitz operators. This talk is based on joint work with Mishko Mitkovski.
Posted September 6, 2024
Last modified October 11, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Laura Menini, Università degli Studi di Roma Tor Vergata
Distance to Instability for LTI Systems under Structured Perturbations
The talk will present a procedure to compute the distance to instability for linear systems subject to structured perturbations, in particular perturbations that affect polynomially the dynamics of the system. The procedure is based on classical notions from stability of linear systems, optimization and algebraic geometry, some of which will be reviewed briefly. The application to the design of fixed-structure controllers to deal with robust control problems will also be outlined, with the goal of choosing the controller which obtains the best conservative estimate of the region of stability. The results will be illustrated on some academic examples.
Posted November 5, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett Hall 233 (simulcasted via Zoom)
Matthew Mizell, LSU
Structures That Arise From Nested Sequences of Flats in Projective and Affine Geometries
In a vector space $V$, take a sequence of subspaces $V_1,V_2,\dots,V_n$ such that $V_1 \subseteq V_2 \subseteq \ldots \subseteq V_n = V$. Color the non-zero elements of $V_1$ green, the elements of $V_2 \backslash V_1$ red, the elements of $V_3 \backslash V_2$ green and so on. We call the resulting set of green elements a target. The study of targets was initiated by Nelson and Nomoto in 2018 for vector spaces over the $2$-element field. In this talk, we will discuss targets over arbitrary finite fields. We will also consider the graph analogue of targets as well as targets over affine geometries. Our main results will characterize each type of target in terms of its forbidden substructures. This is joint work with James Oxley.
Posted October 8, 2024
Last modified November 4, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Michael Allen, Louisiana State University
An infinite family of hypergeometric supercongruences
In a recent series of papers with Brian Grove, Ling Long, and Fang-Ting Tu, we explore the relationship between modular forms and hypergeometric functions in the particular settings of complex, finite, and $p$-adic fields, and unify these perspectives through Galois representations. In this talk, we focus primarily on the $p$-adic aspects, where this relationship arises in the form of congruences between truncated hypergeometric sums and Fourier coefficients of modular forms. Such congruences are predicted to hold modulo $p$ by formal commutative group law, we refer to a congruence modulo a higher power of $p$ as a supercongruence. In this talk, we briefly survey results and methods in the area of supercongruences before establishing an infinite family of supercongruences which hold modulo $p^2$ for all primes in certain arithmetic progressions depending on the parameters of the corresponding hypergeometric functions.
Posted October 22, 2024
Computational Mathematics Seminar
3:30 pm DMC 1034
Jeremy Shahan, Louisiana State University
Shape Optimization with Unfitted Finite Element Methods
We present a formulation of a PDE-constrained shape optimization problem that uses an unfitted finite element method (FEM). The geometry is represented (and optimized) using a level set approach and we consider objective functionals that are defined over bulk domains. For a discrete objective functional (i.e. one defined in the unfitted FEM framework), we derive the exact Frechet, shape derivative in terms of perturbing the level set function directly. In other words, no domain velocity is needed. We also show that the derivative is (essentially) the same as the shape derivative at the continuous level, so is rather easy to compute. In other words, one gains the benefits of both the optimize-then-discretize and discretize-then-optimize approaches.
Posted August 30, 2024
Last modified November 11, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Saumya Jain, Louisiana State University
Gromov norm is directly proportional to the volume
We will prove that the Gromov norm of a compact oriented hyperbolic manifold is directly proportional to its volume.
Posted September 17, 2024
Last modified November 11, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Arka Banerjee, Auburn University
Urysohn 1-width and covers
A metric space has small Urysohn 1-width if it admits a continuous map to a 1-dimensional complex where the preimage of each point has small diameter. An open problem is, if a space's universal cover has small Urysohn 1-width, must the original space also have small Urysohn 1-width? While one might intuitively expect this to be true, there are strange examples that suggest otherwise. In this talk, I will explore the motivations behind this question and discuss some partial progress we have made in understanding it. This is a joint work with H. Alpert and P. Papasoglu.
Posted November 12, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 237
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 4
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted November 12, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 237
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 4
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted October 12, 2024
Last modified October 22, 2024
Robert Fulsche, University of Hannover, Germany
Harmonic analysis on phase space and operator theory
In his paper \emph{Quantum harmonic analysis on phase space} from 1984 (J. Math. Phys.), Reinhard Werner developed a new phase space formalism which allowed for a joint harmonic analysis of functions and operators. Since his reasoning was mostly guided by motivations from the physical side of quantum mechanics, mathematicians ignored this highly interesting contribution for almost 35 years. Only in the last few years, interest in Werner's approach grew and actually yielded a number of interesting and relevant results in time-frequency analysis as well as in operator theory. The speaker, who has been working mostly on the operator theory side of quantum harmonic analysis (QHA), will try to describe the basic features of QHA and how they relate to problems in operator theory. After presenting some basics of the formalism of QHA, we will discuss one application of the audience's choice: Either a result in Fredholm theory, results in commutative operator algebras or a characterization problem of a certain important algebra appearing in QHA.
Posted August 29, 2024
Last modified October 22, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Piernicola Bettiol, Université de Bretagne Occidentale, France
Average Cost Minimization Problems Subject to State Constraints
Optimal control problems involving parameters appear to be a natural framework for some models arising in applications such as aerospace engineering, machine learning, and biology, among many others. According to the nature of the problem (or the model), we may have different minimization criteria; in some circumstances it is more convenient to provide the performance criterion in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this talk, we shall consider pathwise state constraint optimal control problems in which unknown parameters intervene in the dynamics, the cost, the endpoint constraint, and the state constraint. The cost criteria to minimize take the integral form of a given endpoint cost function with respect to a reference probability measure that is defined on the set of unknown parameters. For this class of problems, we shall present the necessary optimality conditions.
Posted September 11, 2024
Last modified October 25, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Michael Novack, Louisiana State University
TBA
Posted November 1, 2024
5:30 pm James E. Keisler Lounge (room 321 Lockett)Actuarial Student Association Meeting
Last meeting of the semester. Pizza will be served.
Posted October 8, 2024
Last modified November 18, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
David Lowry-Duda, ICERM
Murmuration phenomena in number theory
Approximately 2 years ago, a group of number theorists experimenting with machine learning observed unexpected biases in data from elliptic curves. When plotted, these biases loosely resemble gatherings of starlings, leading to the name "murmurations." This now seems to be a very general phenomenon in number theory. Many different families of arithmetic objects exhibit consistent biases. But proving these behaviors has been challenging. In this talk, we'll give several examples of murmuration phenomena, connect these biases to distributions of zeros of L-functions, and describe recent success proving murmurations (especially for modular forms).
Posted October 18, 2024
Computational Mathematics Seminar
3:30 pm DMC 1034
Suhan Zhong, Texas A&M University
Two-stage stochastic programs with polynomial loss function
Two-stage stochastic programs (SPs) with polynomial loss functions serve as a powerful framework for modeling decision-making problems under uncertainty. In this talk, we introduce a two-phase approach to find global optimal solutions for two-stage SPs with continuous decision variables and nonconvex recourse functions. Our method does not only generate global lower bounds for the nonconvex stochastic program, but also yields an explicit polynomial approximation for the recourse function. It is particularly suitable for the case where the random vector follows a continuous distribution or when dealing with a large number of scenarios. Numerical experiments are conducted to demonstrate the effectiveness of our proposed approach.
Posted August 30, 2024
Last modified November 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Samuel Weiner, Louisiana State University
A Survey of Topological Graph Theory
Although graphs are often thought of as strictly combinatorial objects, many substantial developments in graph theory have come by considering their topological properties. For instance, we may define the genus of a graph G to be the minimum integer n such that G embeds into an orientable surface of genus n. Kuratowski's Theorem is a seminal result that precisely determines the class of all genus-2 graphs; a recent result due to Robertson and Seymour characterizes the much broader class of all graphs of bounded genus. We will explore these and other results that lie at the intersection of topology and graph theory. The speaker will assume no prior graph theory knowledge.
Posted November 19, 2024
Probability Seminar Questions or comments?
3:30 pm Lockett 237
Benjamin Fehrman, Louisiana State University
Lectures on Homogenization - Part 5
In these lectures, we will develop a fully rigorous theory of stochastic homogenization for linear elliptic equations, beginning with the periodic case. Applications of homogenization are diverse, and include modeling the conductivity of composites with small-scale defects and the large-scale behavior of passive advected quantities like temperature in turbulent fluid flows. These systems are effectively random, to our eyes, and their study is essentially equivalent to the asymptotic behavior of a diffusion process in a random environment. Our aim is to derive an effective model that provides a good approximation of the original system with high probability.
Posted November 11, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Benjamin Dodson, Johns Hopkins University
Global well-posedness and scattering for the radial, conformal wave equation
In this talk we prove global well-posedness and scattering for the radially symmetric nonlinear wave equation with conformally invariant nonlinearity. We prove this result for sharp initial data.
Posted August 21, 2024
Last modified November 10, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Benedetto Piccoli, Rutgers University, Camden
AMS Fellow, SIAM W. T. and Idalia Reid Prize Awardee
Control Theory in Traffic Applications: 100 Years of Traffic Models
In 1924, in The Quarterly Journal of Economics, Frank H. Knight debated on social costs using an example of two roads, which was the basis of Wardrop’s principle. The author suggested the use of road tolls, and it was probably the first traffic model ever. A few other milestones of a long history include the traffic measurements by Greenshields in 1934, the Lighthill-Whitham-Richards model in the late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to the modern theory of conservation laws on topological graphs with applications to traffic monitoring. The theory requires advanced mathematics, such as BV spaces and Finsler-type metrics on L1. In the late 2000s, this theory was combined with Kalman filtering to deal with traffic monitoring using data from cell phones and other devices. Then we will turn to measure-theoretic approaches for multi-agent systems, which encompass follow-the-leader-type models. Tools from optimal transport allow us to deal with the mean-field limit of controlled equations, representing the action of autonomous vehicles. We will conclude by discussing how autonomy can dissipate traffic waves and reduce fuel consumption, and we will illustrate results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.
Posted November 21, 2024
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom Link
Dillon Mayhew, University of Leeds
Excluded minors for Z3-gainable biased graphs
A biased graph is a graph along with a collection of distinguished cycles, which are said to be balanced. The only rule is that a theta subgraph cannot contain exactly two balanced cycles.Minors of biased graphs work more or less as one would expect: we can delete or contract edges (and delete isolated vertices), and the balanced cycles of the minor are inherited from the larger biased graph.Sometimes the balanced cycles are determined by a gaining function which applies elements of a group to (oriented) edges. We calculate the product of edge labels around a cycle (taking the inverse of a label if that edge is oriented against our direction of travel), and declare a cycle to be balanced if this product is the group identity. If the balanced cycles can be produced in this way via some labeling with elements from the group H, then the biased graph is said to be H-gainable.H-gainable biased graphs form a minor-closed class within the universe of biased graphs, so we naturally ask for a characterisation via excluded minors. This characterisation was completed for the group Z2 by Zaslavsky. We have now completed the characterisation when the group is Z3.More generally, we can postulate a version of Rota's conjecture: when H is a finite group, there are only finitely many excluded-minor biased graphs for the class of H-gainable biased graphs. One might think that this is exactly the same problem as Rota's conjecture for the class of frame matroids or lift matroids arising from H-gainable biased graphs. However, there is no reason to be believe that solving one of these problems will solve the other.This is joint work with Nick Brettell, Rutger Campbell, and Daryl Funk.
Posted November 23, 2024
Probability Seminar Questions or comments?
2:30 pm Lockett 240
Wasiur KhudaBukhsh, University of Nottingham
Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference
We consider a stochastic model of multistage Michaelis--Menten (MM) type enzyme kinetic reactions describing the conversion of substrate molecules to a product through several intermediate species. The high-dimensional, multiscale nature of these reaction networks presents significant computational challenges, especially in statistical estimation of reaction rates. This difficulty is amplified when direct data on system states are unavailable, and one only has access to a random sample of product formation times. To address this, we proceed in two stages. First, under certain technical assumptions akin to those made in the Quasi-steady-state approximation (QSSA) literature, we prove two asymptotic results: a stochastic averaging principle that yields a lower-dimensional model, and a functional central limit theorem that quantifies the associated fluctuations. Next, for statistical inference of the parameters of the original MM reaction network, we develop a mathematical framework involving an interacting particle system (IPS) and prove a propagation of chaos result that allows us to write a product-form likelihood function. The novelty of the IPS-based inference method is that it does not require information about the state of the system and works with only a random sample of product formation times. We provide numerical examples to illustrate the efficacy of the theoretical results. Preprint: https://arxiv.org/abs/2409.06565
Posted August 29, 2024
Last modified December 2, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Jiuya Wang, University of Georgia
Counterexamples for Turkelli's Modification of Malle's Conjecture
Malle's conjecture gives a conjectural distribution of number fields with bounded discriminant. Klueners gives counterexamples of Malle's conjecture, due to the presence of roots of unity in intermediate fields. These types of counterexamples exists in both global function fields and number fields. Turkelli proposes a modification of Malle's conjecture inspired by a function field analogue. We give counterexamples for Turkelli's modified conjecture. We will also talk about the difference of Malle's conjecture on function fields and number fields.
Posted August 30, 2024
Last modified December 2, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Huong Vo, Louisiana State University
Mostow's Rigidity Theorem
Mostow's Rigidity Theorem states that two connected, compact, oriented hyperbolic manifolds of dimension at least 3 that are homotopy equivalent are isometric. In this talk, we will review key steps and finish the proof of this theorem.
Posted August 13, 2024
Last modified November 24, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Karl Johansson, KTH Royal Institute of Technology, Sweden
Fellow of IEEE, IEEE CSS Hendrik W. Bode Lecture Prize Awardee
Machine Learning Components in Cyber-Physical Transport Systems
Advances in sensing, connectivity, computing, and electrification are reshaping the infrastructure for moving people and goods. Research in optimizing and enhancing the resilience of transport systems highlights the broader impact of control technology on mobility. This talk will explore the emerging field of learning-enabled cyber-physical-human systems and discuss some specific examples in intelligent transport. We will show how connected vehicles acting as mobile sensors and actuators can enable traffic predictions and control at a scale never before possible, by learning traffic models using physics-informed machine learning techniques. The complexities of safe interactions between automated and human-driven vehicles will be discussed, emphasizing the integration of formal reasoning methods and the use of tele-operation. The presentation highlights joint work with students, postdocs, and collaborators in academia and industry.
Posted September 4, 2024
Last modified December 10, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Note the new seminar time. Zoom (click here to join)
María Soledad Aronna, Escola de Matematica Aplicada, Brazil
Control of Pest and Disease Dynamics
In this talk, we will discuss some models related to disease control. These models include the optimization of vaccination and testing strategies, as well as systems for biological control of insects and pests. We will demonstrate how optimal control theory and other associated tools aid in analyzing the systems and provide answers to practical questions.
Posted November 8, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Applied Math
Posted November 8, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Algebra
Posted November 8, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Analysis
Posted November 8, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Topology
Posted January 11, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:20 pm Virtual talk: click here to attend on Zoom
Walter Bridges, University of North Texas.
The proportion of coprime fractions in number fields
The ring $\mathbb{Z}[\sqrt{-5}]$ is often one of the first examples students encounter of a ring that is not unique factorization domain. Relatedly, in the number field $\mathbb{Q}(\sqrt{-5})$, we have $$ \frac{1+\sqrt{-5}}{2}=\frac{3}{1-\sqrt{-5}}. $$ Both fractions are reduced, meaning that numerator and denominator do not share any (non-unit) factors in $\mathbb{Z}[\sqrt{-5}]$. However, neither fraction is coprime, in the sense that the numerator and denominator pair do not generate $\mathbb{Z}[\sqrt{-5}]$. In this talk, we will answer the question of how often this phenomenon occurs. That is, we compute the density, suitably defined, of the set of coprime fractions in the set of all reduced fractions in a generic number field. Our answer for $\mathbb{Q}(\sqrt{-5})$ is 80%. We will begin with a review of algebraic number theory, then discuss our notion of density in number fields. Finally, we will show that the density in question may be computed using well-known properties of Hecke L-functions. We intend this talk to be accessible to beginning graduate students.
Posted January 13, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Trinh Tien Nguyen, University of Wisconsin Madison
Boundary Layers in Fluid Dynamics and Kinetic Theory
Abstract: In this talk, I will discuss recent results on Prandtl boundary layer theory in fluid dynamics. We demonstrate that the Prandtl expansion holds for initial data that is analytic near the boundary under the no-slip boundary condition. I will then present a recent result on the validity of the Prandtl expansion from Boltzmann theory, marking an important step toward justifying other types of approximate solutions (arising from fluid dynamics) as macroscopic limits of the kinetic Boltzmann equations.
Posted January 19, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Virtual talk: click here to attend on Zoom
Asimina Hamakiotes, University of Connecticut
Abelian extensions arising from elliptic curves with complex multiplication
Let $K$ be an imaginary quadratic field, and let $\mathcal{O}_{K,f}$ be an order in $K$ of conductor $f \geq 1$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_{K,f}$, such that $E$ is defined by a model over $\mathbb{Q}(j(E))$, where $j(E)$ is the $j$-invariant of $E$. Let $N\geq 2$ be an integer. The extension $\mathbb{Q}(j(E), E[N])/\mathbb{Q}(j(E))$ is usually not abelian; it is only abelian for $N=2,3$, and $4$. Let $p$ be a prime and let $n\geq 1$ be an integer. In this talk, we will classify the maximal abelian extension contained in $\mathbb{Q}(E[p^n])/\mathbb{Q}$.
Posted November 10, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Rushikesh Kamalapurkar, University of Florida
Operator Theoretic Methods for System Identification
Operator representations of dynamical systems on Banach spaces provide a wide array of modeling and analysis tools. In this talk, I will focus on dynamic mode decomposition (DMD). In particular, new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems will be presented. In the SVD approach, dynamic systems are modeled as total derivative operators that operate on reproducing kernel Hilbert spaces (RKHSs). The resulting total derivative operators are shown to be compact provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operators that converges, in norm, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given sample trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and left singular functions of the finite rank operators to those of the total derivative operator. Finally, the convergent SVDs are utilized to construct estimates of the vector field that models the system. The estimated vector fields are shown to be provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems are also discussed. This talk is based in part on joint works [RK23], [RK24], and [RRKJ24] with J.A. Rosenfeld.
Posted January 10, 2025
Last modified January 17, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Suhan Zhong, Texas A&M University
Polynomial Optimization in Data Science
Abstract: Optimization plays a pivotal role in data science. Recent advances in polynomial optimization have introduced innovative methods to solve many challenging problems in this field. In this talk, I will showcase the application of polynomial optimization through the lens of two-stage stochastic models. Additionally, I will provide a brief overview of the underlying theory and discuss potential future research directions.
Posted January 15, 2025
Last modified January 21, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Saber Jafarpour, University of Colorado Boulder
Safety and Resilience of Learning-enabled Autonomous Systems: A Monotone Contracting System Perspective.
Abstract: Learning-enabled autonomous systems are increasingly deployed for decision-making in safety-critical environments. Despite their substantial computational advantages, ensuring the safety and reliability of these systems remains a significant challenge due to their high dimensionality and inherent nonlinearity. In this talk, we leverage tools and techniques from control theory to develop theoretical and algorithmic methods for certifying the safety and robustness of learning-enabled autonomous systems. Our approach investigates safety and resilience from a reachability perspective. We employ contraction and monotone systems theories to develop computationally efficient frameworks for approximating reachable sets of autonomous systems. We demonstrate how these frameworks can be applied to verify and train robust standalone neural networks and to provide run-time safety assurance in systems with learning-based controllers.
Posted December 11, 2024
Last modified January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Akram Alishahi, University of Georgia
Contact invariants in Heegaard Floer homology
Over the past two decades multiple invariants of contact structures have been defined in different variations of Heegaard Floer homology. We will start with an overview of these invariants and their connections. Then, we will discuss one of these invariants that is defined for a contact 3-manifold with a foliated boundary and lives in bordered sutured Floer homology in more details. This is a joint work with Földvári, Hendricks, Licata, Petkova and Vertesi.
Posted December 5, 2024
Last modified January 22, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Ken Ono, University of Virginia
Partitions detect primes
This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Posted December 6, 2024
Last modified January 2, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Harbir Antil, George Mason University
Optimization and Digital Twins
With recent advancements in computing resources and interdisciplinary collaborations, a new research field called Digital Twins (DTs) is starting to emerge. Data from sensors located on a physical system is fed into its DT, the DT in turn help make decisions about the physical system. This cycle then continues for the life-time of the physical system. A typical example is for instance a bridge. In many cases, these problems can be cast as optimization problems with finite or infinite dimensional (partial differential equations) constraints. This talk will provide an introduction to this topic. Special attention will be given to: 1) Optimization algorithms that are adaptive and can handle inexactness, e.g., Trust- Regions and ALESQP; 2) Optimization under uncertainty and tensor train decomposition to overcome the curse of dimensionality; 3) Reduced order modeling for dynamic optimization using randomized compression. Additionally, the DT framework may require coupling mutiphysics / systems / data with very different time scales. Keeping this in mind, a newly introduced notion of barely coupled problems will be discussed. Realistic examples of DTs to identify weakness in structures such as bridges, wind turbines, electric motors, and neuromorphic imaging will be considered.
Posted January 21, 2025
Combinatorics Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett Hall 233
Avin Sunuwar, LSU
Chain theorems on 3-connected graphs
Chain theorems provide a pathway in constructing and analyzing families of graphs. In this seminar, we explore improvements in chain theorems for 3-connected graphs and their subclasses. We discuss an improved version of Tutte’s Wheel Theorem, which enhances algorithmic efficiency by limiting the construction process to extensions of the wheel W4 with restricted operations. Then, we discuss a chain theorem for smoothly 3-connected graphs. Additionally, we present a chain theorem for rooted graphs. These results not only refine classical theorems but also pave the way for further advancements in graph theory and its applications.
Posted January 28, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Federico Glaudo, Institute for Advanced Study, Princeton
A Journey through PDEs and Geometry
This talk will explore a range of intriguing questions that lie at the crossroads of partial differential equations and geometry. Topics include the stability of near-solutions to PDEs, the isoperimetric inequalities on curved spaces, as well as the random matching problem. The aim is to make the ideas accessible and engaging for a broad mathematical audience.
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Megan Fairchild, Louisiana State University
Rachel Meyers, Louisiana State University
Introduction to the h-Cobordism Theorem
We state the h-Cobordism theorem and go over the motivation and background to understand the statement of the theorem. Additionally, we discuss its relevance and impact to the generalized Poincarè conjecture in dimensions 5 and higher.
Posted January 23, 2025
Last modified January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Stoffregen, Michigan State University
Pin(2) Floer homology and the Rokhlin invariant
In this talk, we describe a family of homology cobordism invariants that can be extracted from Pin(2)-equivariant monopole Floer homology (using either Manolescu or Lin's definitions), that have some properties in common with both the epsilon and upsilon invariants in knot Floer homology. We'll show a relationship of this family to questions about torsion in the homology cobordism group, and to triangulation of higher-dimensional manifolds. This is joint work in progress with Irving Dai, Jen Hom, and Linh Truong.
Posted February 5, 2025
Colloquium Questions or comments?
2:30 pm – 3:30 pm Zoom
Ajay Chandra, Imperial College London
An Invitation to Singular Stochastic Partial Differential Equations
Abstract: In this talk I will start by motivating the fundamental importance of singular stochastic partial differential equations in (i) our understanding of the large-scale behaviour of dynamic random systems and (ii) developing a rigorous approach to quantum field theory. I will describe the key mathematical difficulties these equations pose, and sketch how combining analytic, probabilistic, and algebraic arguments have allowed mathematicians to overcome these difficulties and develop a powerful new PDE theory. I’ll also discuss some more recent developments in this area, namely applications to gauge theory and non-commutative probability theory.
Posted November 1, 2024
Last modified January 8, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Ali Zemouche, University of Lorraine, France
Advanced Robust Moving Horizon Estimation Schemes for Nonlinear Systems
This presentation deals with robust stability analysis of moving horizon estimation (MHE) for a class of nonlinear systems. New mathematical tools are introduced, enabling the development of new design conditions to optimize the parameters of the MHE scheme's cost function. These conditions are closely tied to the size of the MHE window and the system's incremental exponential input/output-to-state stability (i-EIOSS) coefficients. To enhance the robustness of the MHE while minimizing the window size, advanced prediction techniques are proposed. Additionally, innovative linear LMI-based methods are presented for synthesizing the i-EIOSS coefficients and prediction gains. The effectiveness of the proposed prediction methods is validated through numerical examples, highlighting their performance improvements.
Posted February 5, 2025
Faculty Meeting Questions or comments?
3:30 pm – 4:30 pm ZoomMeeting of the Professorial Faculty
Posted February 3, 2025
Last modified February 10, 2025
Informal Geometry and Topology Seminar Questions or comments?
12:30 pm
Porter Morgan, University of Massachusetts Amherst
Obtaining exotic 4-manifolds through torus surgery
Let M be a closed, smooth, oriented 4-manifold. In this talk, we’ll explore how to construct an irreducible copy of M using torus surgery; this means that we construct a 4-manifold X that’s homeomorphic to M, but not diffeomorphic to it, and also that X is irreducible in the sense that it can’t be expressed as a non-trivial connect sum. We’ll first describe a general strategy for finding irreducible copies. Then we’ll define torus surgery, and go through an example of building an irreducible copy with this tool. If time permits, we’ll talk about some other surgery techniques that can be used to build irreducible copies.
Posted November 12, 2024
Last modified February 10, 2025
Geometry and Topology Seminar Seminar website
2:30 pm
Porter Morgan, University of Massachusetts Amherst
Irreducible 4-manifolds with order two fundamental group
Let R be a closed, smooth, oriented 4–manifold with order two fundamental group. The works of Freedman and Hambleton-Kreck show that R is determined up to homeomorphism by just a few basic properties. That said, there are often many different manifolds that are homeomorphic to R, but not diffeomorphic to it or each other. In this talk, we’ll describe how to construct irreducible copies of R; roughly speaking, these are smooth manifolds that are homeomorphic to R, and don’t decompose into non-trivial connected sums. We’ll show that if R has odd intersection form and non-negative first Chern number, then in all but seven cases, it has an irreducible copy. We’ll describe some of the techniques used to realize these irreducible smooth structures, including torus surgeries, symplectic fiber sums, and a novel approach to constructing Lefschetz fibrations equipped with free involutions. This is joint work with Mihail Arabadji.
Posted December 2, 2024
Last modified February 7, 2025
Chian Yeong Chuah, Ohio State University
Marcinkiewicz Schur Multiplier Theory for Schatten-p class
The boundedness of Schur Multipliers plays an important role in the study of non-commutative harmonic analysis. In this talk, we provide a Marcinkiewicz type multiplier theory for the Schur multipliers on the Schatten p-classes. This generalizes a previous result of Bourgain for Toeplitz type Schur multipliers and complements a recent result by Conde-Alonso, Gonzalez-Perez, Parcet and Tablate. As a corollary, we obtain a new unconditional decomposition for the Schatten p-classes for p>1. Similar results can also be extended to the case of R^d and Z^d, where d>=2.
Posted February 10, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 233 (Simulcasted via Zoom)
Christine Cho, Louisiana State University
Weak maps and the Tutte polynomial
Let M and N be distinct matroids such that N is the image of M under a rank-preserving weak map. Generalizing results of Dean Lucas, we prove that, for x and y positive, T(M;x,y) \geq T(N;x,y) if and only if x+y \geq xy. We give several consequences of this result related to relative freedom of elements of a matroid.
Posted February 10, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Hongki Jung, Louisiana State University
$\Lambda(p)$--subsets of manifolds
In 1989, Bourgain proved the existence of maximal $\Lambda(p)$--subsets within the collection of mutual orthogonal functions. We shall explore the Euclidean analogue of $\Lambda(p)$—sets through localization. As a result, we construct maximal $\Lambda(p)$--subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. This is joint work with C. Demeter and D. Ryou.
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Krishnendu Kar, Louisiana State University
TBD
Posted February 6, 2025
Last modified February 12, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Neal Stoltzfus, Mathematics Department, LSU
Discrete Laplacians, Ribbon Graphs, and Link Polynomials
The Whitney homology of the independence lattices of the state space of a ribbon graphs supports three independent anti-commuting discrete Laplacians. They relate to the three fundamental combinatorial invariants of independent subsets: rank, nullify and genus. We explore the combinations that give link invariants.
Posted January 20, 2025
Last modified February 10, 2025
Kabe Moen, University of Alabama
New perspectives on the subrepresentation formula
The classical subrepresentation formula establishes that a smooth function is bounded pointwise by the Riesz potential applied to its gradient. This fundamental inequality, combined with the mapping properties of the Riesz potential, leads to the celebrated Gagliardo-Nirenberg-Sobolev inequality, which plays a crucial role in analysis and partial differential equations. In this talk, we show a powerful extension of the subrepresentation formula to several prominent operators in harmonic analysis, including exotic cases such as rough singular integrals and spherical maximal functions. Additionally, we uncover some new structural properties of subrepresentation formulas, including an openness property and an equivalence with weighted Sobolev inequalities and isoperimetric inequalities.
Posted December 23, 2024
Last modified January 10, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Carsten Scherer, University of Stuttgart, Germany
IEEE Fellow
Robust Control and the Design of Controllers for Optimization
Recent years have witnessed a renewed interest in considering optimization algorithms as feedback systems. This viewpoint turns, for example, the analysis of the convergence properties of a first order algorithm into a problem of stability analysis of a Lure system. In this talk we highlight why advanced methods in robust control play a key role for developing unprecedented tools to analyze the convergence properties of first order algorithms for solving strongly convex programs. In contrast to alternative approaches, we reveal that the proposed avenue permits not only the analysis but also the systematic design of optimization algorithms using convex semi-definite programming.
Posted October 18, 2024
1:00 pm – 4:00 pm Saturday, February 22, 2025 Digital Media Center TheatreFinite Element Rodeo
https://www.cct.lsu.edu/finite_element2025
Posted February 17, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Yixuan Huang, Vanderbilt University
Hierarchy of trees, walks, and Hamiltonicity of products
A spanning t-tree is a spanning tree of maximum degree at most t. A spanning t-walk is a spanning closed walk visiting every vertex at most t times. Spanning t-trees and spanning t-walks are generalizations of Hamiltonian paths and Hamiltonian cycles. Jackson and Wormald (1990) showed that the existence of spanning t-walks implies the existence of spanning t-trees, which again implies the existence of spanning (t+1)-walks. In this talk, we go through results on the existence of these two objects and introduce some results on Hamiltonicity of products of graphs that can be added to this hierarchy.
Posted January 26, 2025
Last modified February 24, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Akio Nakagawa, Kanazawa University
Hypergeometric functions over finite fields
In this talk, I will explain about Otsubo’s definition of hypergeometric functions over finite fields, and I will introduce how the confluent hypergeometric functions over finite fields are useful by showing a transformation formula for Appell–Lauricella functions over finite fields. If time allows, I will introduce my recent work on relations between hypergeometric functions and algebraic varieties.
Posted November 12, 2024
Last modified February 26, 2025
Dave Auckly, Kansas State University
Die on a grid — a twisted story
We will begin by presenting an infinite collection of puzzles with dice. We will see that solutions to these puzzles lead one to explore geometry on interesting spaces where things get twisted.
Posted February 23, 2025
Last modified February 24, 2025
Hamed Musavi, King's College London
An overview on the recent progress on quantitative Szemeredi Theorems
In this talk, we will start with introducing the classical (qualitative) Ramsey-type Theorems in Additive Combinatorics such as Roth, Sarkozy and Szemeredi Theorems. Then we propose the quantitative problems and a motivation behind their importance. Next, we mention a few recent results on these problems. Finally if time permits, we will talk about ideas in the proofs. This is a joint work with Ben Krause, Terence Tao, and Joni Teravainen.
Posted January 14, 2025
Last modified February 18, 2025
Geometry and Topology Seminar Seminar website
3:30 pm
Dave Auckly, Kansas State University
Restrictions on the genus of trivial families of surfaces in twisted families of 4-manifolds
Several notions of equivalence in topology may be expressed via the existence of families. Thus, asking when an untwisted family of surfaces can be placed in a twisted family of manifolds in a natural question. This talk will describe a generalized adjunction inequality for families.
Posted December 8, 2024
Last modified February 24, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
John Baras, University of Maryland
Fellow of AAAS, AMS, IEEE, and SIAM
Robust Machine Learning, Reinforcement Learning and Autonomy
Robustness is a fundamental concept in systems science and engineering. It is a critical consideration in inference and decision-making problems. It has recently surfaced again in the context of machine learning (ML), reinforcement learning (RL) and artificial intelligence (AI). We describe a novel and unifying theory of robustness for ML/RL/AI emanating from our much earlier fundamental results on robust output feedback control for general systems. We briefly summarize this theory and the universal solution it provides consisting of two coupled HJB equations. These earlier results rigorously established the equivalence of three seemingly unrelated problems: the robust output feedback control problem, a partially observed differential game, and a partially observed risk sensitive stochastic control problem. We first show that the “four block” view of the above results leads naturally to a similar formulation of the robust ML problem, and to a rigorous path to analyze robustness and attack resiliency in ML. Then we describe a recent risk-sensitive approach, using an exponential criterion in deep learning, that explains the convergence of stochastic gradients despite over-parametrization. Finally, we describe our most recent results on robust and risk sensitive RL for control, using exponential rewards, that emerge from our earlier theory, with the important new extension that the models are now unknown. We show how all forms of regularized RL can be derived from our theory, including KL and entropy regularization, a relation to probabilistic graphical models, and distributional robustness. The deeper reason for this unification emerges: it is the fundamental tradeoff between performance and risk measures in decision making, via rigorous duality. We close with open problems and future research directions.
Posted February 24, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom (email zhiyuw at lsu.edu for Zoom link)
Tung Nguyen, Princeton University
Induced subdivisions and polylogarithmic chromatic number
We discuss a proof that for every graph H, every n-vertex graph with no induced subdivision of H and with bounded clique number has chromatic number at most polylog(n). This extends a result of Fox and Pach that similar polylogarithmic bounds hold for all string graphs, and is close to optimal as there are triangle-free n-vertex string graphs with chromatic number at least loglog n. Joint work with Alex Scott and Paul Seymour.
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Huong Vo, Louisiana State University
TBD
Posted November 21, 2024
Last modified March 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Christoph Fischbacher, Baylor University
Non-selfadjoint operators with non-local point interactions
In this talk, I will discuss non-selfadjoint differential operators of the form $i\frac{d}{dx}+V+k\langle \delta,\cdot\rangle$ and $-\frac{d^2}{dx^2}+V+k\langle \delta,\cdot\rangle$, where $V$ is a bounded complex potential. The additional term, formally given by $k\langle \delta,\cdot\rangle$, is referred to as ``non-local point interaction" and has been studied in the selfadjoint context by Albeverio, Cojuhari, Debowska, I.L. Nizhnik, and L.P. Nizhnik. I will begin with a discussion of the spectrum of the first-order operators on the interval and give precise estimates on the location of the eigenvalues. Moreover, we will show that the root vectors of these operators form a Riesz basis. If the initial operator is dissipative (all eigenvalues have nonnegative imaginary part), I will discuss the possibility of choosing the non-local point interaction in such a way that it generates a real eigenvalue even if the potential is very dissipative. After this, I will focus on the dissipative second order-case and show similar results on constructing realizations with a real eigenvalue. Based on previous and ongoing collaborations with Matthias Hofmann, Andrés Lopez Patiño, Sergey Naboko, Danie Paraiso, Chloe Povey-Rowe, Monika Winklmeier, Ian Wood, and Brady Zimmerman.
Posted February 24, 2025
Combinatorics Seminar Questions or comments?
10:30 am Lockett Hall 233
James "Dylan" Douthitt, Louisiana State University
Induced-minor-closed classes of matroids (dissertation defense)
Abstract: A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when $q=2$ is distinctive. Additionally, we show that the class of $GF(2)$-chordal matroids coincides with the class of binary matroids that have none of $M(K_4)$, $M^*(K_{3,3})$, or $M(C_n)$ for $n\geq 4$ as a flat. We also show that $GF(q)$-chordal matroids can be characterized by an analogous result to Rose's 1970 characterization of chordal graphs as those that have a perfect elimination ordering of vertices. We then describe the classes of binary matroids with pairs from the set $\{M(C_4),M(K_4\backslash e),M(K_4),F_7\}$ as excluded induced minors. Additionally, we prove structural lemmas toward characterizing the class of binary matroids that do not contain $M(K_4)$ as an induced minor.
Posted October 14, 2024
Last modified February 28, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Thursday, March 6, 2025 Lockett 232
Alexandru Hening, Texas A&M University
Stochastic Population Dynamics in Discrete Time
I will present a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time stochastic difference equations that can include population structure, eco-environmental feedback or other internal or external factors. Using the general theory, I will showcase some interesting examples. I will end my talk by explaining how the population size at equilibrium is influenced by environmental fluctuations.
Posted March 9, 2025
Mathematical Physics and Representation Theory Seminar
12:30 pm – 1:20 pm 233 Lockett Hall
David Boozer, Indiana University
Student Seminar on Instanton Homology and Foam Evaluations
This is to help prepare graduate students for David Boozer's talk at 2:30pm on the same day. He will discuss some of the basic definitions behind his 2:30pm talk and take questions from graduate students on the objects of study in his talk.
Posted February 10, 2025
Last modified February 24, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm 233 Lockett Hall
David Boozer, Indiana University
The combinatorial and gauge-theoretic foam evaluation functors are not the same
Kronheimer and Mrowka have outlined a new approach that could potentially lead to the first non-computer based proof of the four-color theorem. Their approach relies on a functor J-sharp, which they define using gauge theory, from a category of webs in R^3 to the category of finite-dimensional vector spaces over the field of two elements. They have also suggested a possible combinatorial replacement J-flat for J-sharp, which Khovanov and Robert proved is well-defined on a subcategory of planar webs. We exhibit a counterexample that shows the restriction of the functor J-sharp to the subcategory of planar webs is not the same as J-flat.
Posted February 3, 2025
Last modified March 10, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Emmanuel Astante, Louisiana State University
Rota's conjecture and Geometric Lattices
Rota defined homology groups for certain subsets, called cross-cuts, of a lattice. He showed that the value of the Euler characteristic associated with this homology theory depends only on the lattice, not on the choice of the cross-cut. It was conjectured that the homology groups themselves depend only on the lattice. First, we will prove Rota's conjecture. Using this result, we determine the structure of the homology groups of an important class of lattices called geometric lattices.
Posted March 4, 2025
Last modified March 10, 2025
Geometry and Topology Seminar Seminar website
2:30 pm Lockett 233
Maarten Mol, University of Toronto
Constructibility of momentum maps and variation of singular symplectic reduced spaces (Joint with Mathematical Physics and Representation Theory Seminar)
Proper maps in various categories studied in singularity theory (for example, the real analytic category) are known to be constructible, in the sense that the image of the map can be stratified in such a way that the map is a topological fiber bundle over each stratum. Such stratifications provide insight into how the fibers of the map vary. In this talk we will discuss the existence of such a stratification for momentum maps of Hamiltonian Lie group actions (a natural class of maps studied in symplectic/Poisson geometry), which provides insight into how the so-called symplectic reduced spaces of the Hamiltonian action vary. Along the way we will also try to give an overview of some more classical results on the geometry of such maps.
Posted February 10, 2025
Last modified March 9, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Maarten Mol, University of Toronto
Constructibility of momentum maps and variation of singular symplectic reduced spaces
Proper maps in various categories studied in singularity theory (for example, the real analytic category) are known to be constructible, in the sense that the image of the map can be stratified in such a way that the map is a topological fiber bundle over each stratum. Such stratifications provide insight into how the fibers of the map vary. In this talk we will discuss the existence of such a stratification for momentum maps of Hamiltonian Lie group actions (a natural class of maps studied in symplectic/Poisson geometry), which provides insight into how the so-called symplectic reduced spaces of the Hamiltonian action vary. Along the way we will also try to give an overview of some more classical results on the geometry of such maps.
Posted February 19, 2025
Last modified March 10, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Justin Holmer, Brown University
Dynamics of Solitary Waves
Solitary waves arise as exact coherent structures in a range of nonlinear wave equations, including the nonlinear Schrödinger, Korteweg–de Vries, and Benjamin–Ono equations. These equations have broad applications in areas such as water wave theory, plasma physics, and condensed matter physics. When certain types of perturbations are introduced, the solitary wave retains its overall form while its shape and position adjust to accommodate the new conditions. In this talk, I will present some theoretical results on the modulation of solitary wave profiles under such perturbations, supported by numerical simulations that illustrate and validate these findings.
Posted March 12, 2025
Probability Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (See the Control Seminar Advertisement for the link.)
Serdar Yuksel, Queen’s University, Canada
Robustness to Approximations and Learning in Stochastic Control via a Framework of Kernel Topologies
Stochastic kernels represent system models, control policies, and measurement channels, and thus offer a general mathematical framework for learning, robustness, and approximation analysis. To this end, we will first present and study several kernel topologies. These include weak* (also called Borkar) topology, Young topology, kernel mean embedding topologies, and strong convergence topologies. Convergence, continuity, and robustness properties of optimal cost for models and policies (viewed as kernels) will be presented in both discrete-time and continuous-time stochastic control. For models viewed as kernels, we study robustness to model perturbations, including finite approximations for discrete-time models and robustness to more general modeling errors and study the mismatch loss of optimal control policies designed for incorrect models applied to a true system, as the incorrect model approaches the true model under a variety of kernel convergence criteria. In particular, we show that the expected induced cost is robust under continuous weak convergence of transition kernels. Under stronger Wasserstein or total variation regularity, a modulus of continuity is also applicable. As applications of robustness under continuous weak convergence via data-driven model learning, (i) robustness to empirical model learning for discounted and average cost criteria is obtained with sample complexity bounds, and (ii) convergence and near optimality of a quantized Q-learning algorithm for MDPs with standard Borel spaces, which we show to be converging to an optimal solution of an approximate model under both discounted and average cost criteria, is established. In the context of continuous-time models, we obtain counterparts where we show continuity of cost in policy under Young and Borkar topologies, and robustness of optimal cost in models including discrete-time approximations for finite horizon and infinite-horizon discounted/ergodic criteria. Discrete-time approximations under several criteria and information structures will then be obtained via a unified approach of policy and model convergence. This is joint work with Ali D. Kara, Somnath Pradhan, Naci Saldi, and Tamas Linder.
Posted December 22, 2024
Last modified March 5, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Serdar Yuksel, Queen’s University, Canada
Robustness to Approximations and Learning in Stochastic Control via a Framework of Kernel Topologies
Stochastic kernels represent system models, control policies, and measurement channels, and thus offer a general mathematical framework for learning, robustness, and approximation analysis. To this end, we will first present and study several kernel topologies. These include weak* (also called Borkar) topology, Young topology, kernel mean embedding topologies, and strong convergence topologies. Convergence, continuity, and robustness properties of optimal cost for models and policies (viewed as kernels) will be presented in both discrete-time and continuous-time stochastic control. For models viewed as kernels, we study robustness to model perturbations, including finite approximations for discrete-time models and robustness to more general modeling errors and study the mismatch loss of optimal control policies designed for incorrect models applied to a true system, as the incorrect model approaches the true model under a variety of kernel convergence criteria. In particular, we show that the expected induced cost is robust under continuous weak convergence of transition kernels. Under stronger Wasserstein or total variation regularity, a modulus of continuity is also applicable. As applications of robustness under continuous weak convergence via data-driven model learning, (i) robustness to empirical model learning for discounted and average cost criteria is obtained with sample complexity bounds, and (ii) convergence and near optimality of a quantized Q-learning algorithm for MDPs with standard Borel spaces, which we show to be converging to an optimal solution of an approximate model under both discounted and average cost criteria, is established. In the context of continuous-time models, we obtain counterparts where we show continuity of cost in policy under Young and Borkar topologies, and robustness of optimal cost in models including discrete-time approximations for finite horizon and infinite-horizon discounted/ergodic criteria. Discrete-time approximations under several criteria and information structures will then be obtained via a unified approach of policy and model convergence. This is joint work with Ali D. Kara, Somnath Pradhan, Naci Saldi, and Tamas Linder.
Posted January 20, 2025
1:00 pm – 3:30 pm Saturday, March 15, 2025 Tulane UniversityScientific Computing Around Louisiana (SCALA) 2025
http://www.math.tulane.edu/scala2025/index.html
Posted March 10, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233 (Simulcast via Zoom)
Tan Nhat Tran, Binghamton University
Inductive and Divisional Posets: A Study of Poset Factorability
We introduce and study the notion of inductive posets and their superclass, divisionalposets, inspired by the concepts of inductive and divisional freeness for central hyperplane arrangements. A poset is called factorable if its characteristic polynomial has all positive integer roots. Motivated by this, we define inductive and divisional abelian (Lie group) arrangements, with their posets of layers serving as primary examples. Our first main result shows that every divisional poset is factorable. The second result establishes that the class of inductive posets includes strictly supersolvable posets, a class recently introduced by Bibby and Delucchi (2024), which extends the classical result by Jambu and Terao (1984) that every supersolvable hyperplane arrangement is inductively free. Finally, we present an application to toric arrangements, proving that the toric arrangement defined by any ideal of a root system of type A, B, or C, with respect to the root lattice, is inductive. This work is joint with R. Pagaria (Bologna), M. Pismataro (Bologna), and L. Vecchi (KTH).
Posted March 12, 2025
Probability Seminar Questions or comments?
2:30 pm Lockett 232
Hye-Won Kang, University of Maryland, Baltimore County
Multiscale approximations in stochastic reaction networks
In this talk, I will discuss stochastic modeling and approximation techniques for chemical reaction networks. Stochastic effects can play a crucial role in biological and chemical processes, particularly when certain species exist in low copy numbers. A common stochastic model for such systems is the continuous-time Markov jump process. However, due to the large and nonlinear nature of chemical reaction networks, obtaining closed-form solutions for the desired statistical properties is often challenging. I will introduce multiscale approximation methods designed to reduce the complexity of these networks by considering various scales in species copy numbers and reaction rate constants. For each relevant time scale, we derive a simpler limiting model that approximates the behavior of the full model over specific time intervals. Additionally, I will explore the asymptotic behavior of the error between the full model and the limiting model. Throughout the talk, I will demonstrate the application of these multiscale approximation methods to several examples, highlighting their effectiveness in simplifying the analysis of complex systems.
Posted February 10, 2025
Last modified March 13, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Monday, March 17, 0025 Lockett 233
Sam Gunningham, Montana State University
Geometric Satake Revisited
The geometric Satake equivalence is a fundamental result in the geometric Langlands program. It can be understood as a kind of Fourier transform, relating different flavors of sheaves on a dual pair of spaces. Just like the usual Fourier transform, the equivalence exchanges the structures of convolution and pointwise product on each side. In this talk, I will discuss a circle of ideas relating pointwise tensor product of sheaves on the affine Grassmannian, the Knop-Ngo action for the group scheme of regular centralizers, and Moore-Tachikawa varieties. This builds on past joint work with D. Ben-Zvi and some current work in progress with D. Ben-Zvi and S. Devalapurkar.
Posted January 28, 2025
Last modified March 12, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Eun Hye Lee, Texas Christian University
Automorphic form twisted Shintani zeta functions over number fields
In this talk, we will be exploring the analytic properties of automorphic form twisted Shintani zeta functions over number fields. I will start by stating some basic facts from classical Shintani zeta functions, and then we will take a look at the adelic analogues of them. Joint with Ramin Takloo-Bighash.
Posted February 3, 2025
Last modified March 17, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Saumya Jain, Louisiana State University
Handle Trading
Equipped with the tools developed in the previous talks, we will begin by outlining the idea of the proof of the h-cobordism theorem. We will see that if the algebraic "d-pairing" can be realized geometrically, then the proof follows. To this end, we will explore a way to handle low and high handles, introducing handle-trading.
Posted March 10, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Scott Baldridge, Louisiana State University
A new way to prove the four color theorem using gauge theory
In this talk, I show how ideas coming out of gauge theory can be used to prove that certain configurations in the list of "633 unavoidable's" are reducible. In particular, I show how to prove the most important initial example, the Birkhoff diamond (four “adjacent" pentagons), is reducible using our filtered $3$- and $4$-color homology. In this context reducible means that the Birkhoff diamond cannot show up as a “tangle" in a minimal counterexample to the 4CT. This is a new proof of a 111-year-old result that is a direct consequence of a special (2+1)-dimensional TQFT. I will then indicate how the ideas used in the proof might be used to reduce the unavoidable set of 633 configurations to a much smaller set. This is joint work with Ben McCarty.
Posted February 12, 2025
Last modified March 6, 2025
Hye-Won Kang, University of Maryland, Baltimore County
Deterministic and Stochastic Modeling of Chemical Reactions in Biology
In this talk, I will introduce how mathematical models are used to describe chemical reactions. Reaction networks play a key role in various fields, including systems biology, population dynamics, epidemiology, and molecular and cellular biology. We will start by exploring models based on the law of mass action, where chemical species interact in a well-mixed environment, and their concentrations change over time according to differential equations. However, when certain species exist in low quantities, random fluctuations can significantly impact the system's behavior. In such cases, a stochastic model--using a continuous-time Markov jump process--better captures the discrete and probabilistic nature of reaction events. To illustrate the differences between deterministic and stochastic approaches, I will present simple examples, including enzyme kinetics, and compare their dynamic behaviors. For systems that are spatially distributed, we can describe the movement and interaction of chemical species using reaction-diffusion partial differential equations. When some species have low molecular counts, we can extend stochastic models by dividing the spatial domain into smaller regions, assuming each region is well-mixed. I will also introduce several examples of spatially-distributed systems, including applications in developmental biology.
Posted December 9, 2024
Last modified March 14, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Serkan Gugercin, Virginia Tech
What to Interpolate for L2 Optimal Approximation: Reflections on the Past, Present, and Future
In this talk, we revisit the L2 optimal approximation problem through various formulations and applications, exploring its rich mathematical structure and diverse implications. We begin with the classical case where the optimal approximant is a rational function, highlighting how Hermite interpolation at specific reflected points emerges as the necessary condition for optimality. Building on this foundation, we consider extensions that introduce additional structure to rational approximations and relax certain restrictions, revealing new dimensions of the problem. Throughout, we demonstrate how Hermite interpolation at reflected points serves as a unifying theme across different domains and applications.
Posted March 17, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Zach Walsh, Auburn University
Delta-Wye exchange for matroids over pastures
Delta-Wye exchange is a fundamental graph operation that preserves many natural embeddability properties of graphs. This operation generalizes to matroids, and preserves many natural representability properties of matroids. We will present a result showing that Delta-Wye exchange preserves matroid representability over any pasture, which is an algebraic object that generalizes partial fields and hyperfields. This is joint work with Matt Baker, Oliver Lorscheid, and Tianyi Zhang.
Posted February 3, 2025
Last modified March 24, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Peter Ramsey, Louisiana State University
The Orlik-Solomon Algebra and the Cohomology Ring of Hyperplane Arrangements
A hyperplane is a subspace of codimension one in a given vector space. A finite collection of hyperplanes is called a hyperplane arrangement. The compliment of such an arrangement in complex space defines a connected manifold whose topology can be studied via its cohomology ring. A fundamental result by Brieskorn, Orlik, and Solomon shows that this cohomology ring can be computed in a purely combinatorial way using the Orlik-Solomon Algebra. In this talk, we will explore this construction and, if time permits, discuss its implications for the Poincaré polynomial.
Posted March 26, 2025
Geometry and Topology Seminar Seminar website
2:30 pm – 3:30 pm Lockett 233
Scott Baldridge, Louisiana State University
A new way to prove the four color theorem using gauge theory, Part 2
This is a continuation of last week’s talk in which we explain the definition of the homology theory used to prove that Birkhoff’s diamond is reducible. I will quickly summarize last week's discussion before heading into new material, so people can attend this week even if they couldn’t attend last week. This is joint work with Ben McCarty at University of Memphis.
Posted March 21, 2025
Probability Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 237
Barbara Rüdiger, Bergische Universität Wuppertal, Germany
Identification and existence of Boltzmann processes
A stochastic differential equation of the McKean-Vlasov type is identified such that its Fokker-Planck equation coincides with the Boltzmann equation. Its solutions are called Boltzmann processes. They describe the dynamics (in position and velocity) of particles expanding in vacuum in accordance with the Boltzmann equation. Given a good solution of the Boltzmann equation, the existence of solutions to the McKean-Vlasov SDE is established for the hard sphere case. This is a joint work with P. Sundar.
Posted March 25, 2025
3:00 pm – 4:50 pm Lockett 243Beamer Presentation
Join us for a Beamer Presentation where we'll explore how to style and organize Beamer slides, share tips to enhance your presentations, and introduce helpful drawing tools.
Posted March 21, 2025
Last modified March 25, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note the Special Earlier Seminar Time For Only This Week. This is a Zoom Seminar. Zoom (click here to join)
Denis Dochain, Université Catholique de Louvain
IEEE Fellow, IFAC Fellow
Automatic Control and Biological Systems
This talk aims to give an overview of more than 40 years of research activities in the field of modelling and control of biological systems. It will cover different aspects of modelling, analysis, monitoring and control of bio-systems, and will be illustrated by a large variety of biological systems, from environmental systems to biomedical applications via food processes or plant growth.
Posted March 21, 2025
Combinatorics Seminar Questions or comments?
11:30 am – 12:30 pm Zoom Link
Jorn van der Pol, University of Twente
Turán densities for matroid basis hypergraph
What is the maximum number of bases of an n-element, rank-r matroid without a given uniform matroid U as a minor? This question arises in the problem of determining the Turán density of daisy-hypergraphs. Ellis, Ivan, and Leader recently showed that this density is positive, thus disproving a conjecture by Bollobás, Leader, and Malvenuto. Their construction is a matroid basis hypergraph, and we show that their construction is best-possible within the class of matroid basis hypergraphs. This is joint work with Zach Walsh and Michael C. Wigal.
Posted March 28, 2025
until Sunday, March 30, 2025Southern Regional Number Theory Conference
The conference will take place from Saturday, March 29th to Sunday, March 30th at Coates Hall, LSU, and also streamed over Zoom. The talk information and zoom links are at our website: https://www.math.lsu.edu/~srntc/nt2025/schedule.html
Posted March 16, 2025
Last modified April 2, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Justin Lanier, University of Sydney
Twisting cubic rabbits
A polynomial can be viewed as a branched cover of the sphere over itself that is compatible with a complex structure. If handed a topological branched cover of the sphere, we can ask whether it can arise from a polynomial, and if so, which one? In 2006, Bartholdi and Nekrashevych used group theoretic methods to explicitly solve this problem in certain special cases, including Hubbard’s twisted rabbit problem. Using a combinatorial topology approach that draws from the theory of mapping class groups, we solve an infinite family of twisted polynomial problems that are cubic generalizations of Hubbard’s twisted rabbit problem. This is joint work with Becca Winarski.
Posted March 31, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Be'eri Greenfeld , University of Washington
Complexity and Growth of Infinite Words and Algebraic Structures
Given an infinite word (for example, 01101001$\ldots$), its complexity function counts, for each n, the number of distinct subwords of length n. A longstanding open problem is the "inverse problem": Which functions $f:\mathbb N\to \mathbb N$ arise as complexity functions of infinite words? We resolve this problem asymptotically, showing that, apart from submultiplicativity and a classical obstruction found by Morse and Hedlund in 1938, there are essentially no further restrictions. We then explore parallels and contrasts with the theory of growth of algebras, drawing on noncommutative constructions associated with symbolic dynamical systems.
Posted February 3, 2025
Last modified April 7, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Adithyan Pandikkadan, Louisiana State University
Whitney Trick
In the previous talk, we outlined the proof of the h-cobordism theorem. The key step is realizing the algebraic intersection number +1 between the attaching sphere of the k-handle and the belt sphere of the (k+1)-handle as an actual geometric intersection. Achieving this requires eliminating pairs of intersection points with opposite signs by the "Whitney Trick". In this talk, we will focus on understanding the "Whitney Trick" in detail and how it enables these critical geometric manipulations.
Posted March 8, 2025
Last modified March 9, 2025
Tomoyuki Kakehi, University of Tsukuba
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and call the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows. {\bf Theorem.} We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution. We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
Posted March 9, 2025
Last modified April 9, 2025
Tomoyuki Kakehi, University of Tsukuba
Inversion formulas for Radon transforms and mean value operators on the sphere
This talk consists of two parts. In the first part, we explain the Radon transfrom associated with a double fibration briefly and then we introduce several inversion formulas. In the second part, we deal with the mean value operator $M^r$ on the sphere. Here we define $M^r: C^{\infty} (\mathbb{S}^n) \to C^{\infty} (\mathbb{S}^n)$ by $$ M^r f (x) = \frac{1}{\mathrm{Vol} (S_r (x))} \int_{y \in S_r (x)} f(y) d\mu(y), \qquad f \in C^{\infty} (\mathbb{S}^n), $$ where $S_r (x)$ is the geodesic sphere with radius $r$ and center $x$ and $d\mu$ is the measure on $S_r (x)$ induced from the canonical measure on $\mathbb{S}^n$. We will give conditions on $r$ for $M^r$ being injective or surjective. For example, in the case $n=3$, $M^r$ is injective but not surjective if and only if $r/\pi$ is a Liouville number. We will also give some related results on Gegenbauer polynomials. This is a joint work with J. Christensen, F. Gonzalez, and J. Wang.
Posted November 7, 2024
Last modified March 13, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Irena Lasiecka, University of Memphis
AACC Bellman Control Heritage Awardee, AMS Fellow, SIAM Fellow, and SIAM Reid Prize Awardee
Mathematical Theory of Flow-Structure Interactions
Flow-structure interactions are ubiquitous in nature and in everyday life. Flow or fluid interacting with structural elements can lead to oscillations, hence impacting stability or even safety. Thus problems such as attenuation of turbulence or flutter in an oscillating structure (e.g., the Tacoma bridge), flutter in tall buildings, fluid flows in flexible pipes, nuclear engineering flows about fuel elements, and heat exchanger vanes are just a few prime examples of relevant applications which place themselves at the frontier of interests in applied mathematics. In this lecture, we shall describe mathematical models describing the phenomena. They are based on a 3D linearized Euler equation around unstable equilibria coupled to a nonlinear dynamic elasticity on a 2D manifold. Strong interface coupling between the two media is at the center of the analysis. This provides for a rich mathematical structure, opening the door to several unresolved problems in the area of nonlinear PDEs, dynamical systems, related harmonic analysis, and differential geometry. This talk provides a brief overview of recent developments in the area, with a presentation of some new methodology addressing the issues of control and stability of such structures. Part of this talk is based on recent work with D. Bonheur, F. Gazzola and J. Webster (in Annales de L’Institute Henri Poincare Analyse from 2022), work with A. Balakrishna and J. Webster (in M3AS in 2024), and also work completed while the author was a member of the MSRI program "Mathematical problem in fluid dynamics" at the University of California Berkeley (sponsored by NSF DMS -1928930).
Posted April 9, 2025
Faculty Meeting Questions or comments?
12:30 pm – 1:20 pm ZoomMeeting of the Tenured Faculty
Posted January 21, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom Link
Joseph Bonin, George Washington University
Results on positroids from the perspective of structural matroid theory
A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over $\mathbb{R}$ with the property that the determinant of each $r$ by $r$ submatrix is nonnegative. Positroids are commonly studied through the lens of algebraic combinatorics, where a fixed linear order on the ground set is regarded as part of the positroid. We focus on the matroid structure per se, without a priori fixing a linear order on the ground set. A number of earlier characterizations of positroids involve connected flats and non-crossing partitions; we provide a new characterization of a similar flavor and discuss some of its applications. One application is finding conditions under which two positroids can be glued together along a common restriction, in the freest way possible, to yield another positroid: for instance, if $M$ and $N$ are positroids and the intersection of their ground sets is an independent set and a set of clones in both $M$ and $N$, then the free amalgam of $M$ and $N$ is a positroid (that encompasses parallel connections and much more). Also, the class of positroids is minor-closed, and we identify many multi-parameter infinite families of excluded minors for this class, while more excluded minors remain to be discovered.
Posted April 12, 2025
12:00 pm – 1:30 pm Keisler Lounge, Lockett Hall 3rd FloorLife after a Ph.D!
What’s harder than finishing a Ph.D.? Probably finding a job you truly enjoy and that pays well. If you’re wondering what comes after grad school, join the LSU SIAM Chapter for a Job Panel on Monday, April 14, from 12:00–1:30 PM in Keisler Lounge. Our panel — including Prof. Shipman, Dr. Nadejda Drenska, Casey Cavanaugh, and graduate students Jeremy Shanan, Dylan Douthitt, and Christian Ennis — will share insights on the job search process, from applications and interviews to networking and career paths in academia and industry.
Posted February 21, 2025
Last modified April 8, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
John Jairo Lopez, Tulane University
Riemann-Hilbert Approach to the Asymptotic Distribution of Zeros of Orthogonal Polynomials
Orthogonal polynomials possess a variety of properties and characterizations. For instance, it is well known that the zeros of a family of orthogonal polynomials with respect to a weight function \( w(x) \) supported on an interval \( (a,b) \) are all distinct and lie within the interval. This talk will introduce the Riemann-Hilbert problem characterization of orthogonal polynomials, which will then be used to obtain asymptotic information about the polynomials and their zeros. In particular, we will consider Jacobi polynomials \( p_n(x) = p_n^{(\alpha_n,\beta_n)}(x) \), with varying parameters \( \alpha_n \) and \( \beta_n \) in the weight function \[ w(x;\alpha,\beta) = (1-x)^\alpha(1+x)^\beta. \] In the classical case the parameters satisfy \( \alpha, \beta > -1 \). By analytic continuation in the parameters \( \alpha \) and \( \beta \), these polynomials can be studied for more general values. However, when \( \alpha \le -1 \) or \( \beta \le -1 \), the classical orthogonality property on \([-1,1]\) does not hold, and consequently, the zeros may no longer be real or simple. We will see how the Riemann-Hilbert formulation can be extended beyond the classical case to study the asymptotics and zeros of these polynomials. This talk is based on joint work with Victor Moll and Kenneth McLaughlin. (Host: Stephen Shipman)
Posted January 26, 2025
Last modified April 14, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Kairi Black, Duke University
How might we generalize the Kronecker-Weber Theorem?
Hilbert's Twelfth Problem asks for a generalization of the Kronecker-Weber Theorem: cyclotomic units generate the abelian extensions of $\mathbb{Q}$, but what about for other ground fields? We consider a number field $K$ with exactly one complex embedding. In the 1970s, Stark conjectured formulas for (the absolute values of) units inside abelian extensions of $K$. We refine Stark's conjectures with a proposed formula for the units themselves, not just their absolute values.
Posted April 12, 2025
LSU AWM Student Chapter LSU AWM Student Chapter Website
12:30 pm – 1:30 pm Keisler Lounge, Lockett 3rd FloorAutomation Workshop: Streamline Your TA Duties with Python and Excel!
Join the LSU AWM Student Chapter for a hands-on workshop designed to help Math 1021 instructors and graduate TAs save time and stay organized. Whether you're looking to automate end-of-semester reports or integrate Excel and Python into your teaching workflow. This session, led by AWM officer Christian Ennis, will walk you through two practical Python tools: one for generating end-of-semester data sheets and another for classifying lab participation grades based on passing thresholds. We'll also discuss ideas for streamlining other Math 1021 tasks and explore ways to optimize workflows in courses you teach as a TA.
Posted February 3, 2025
Last modified April 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Matthew Lemoine, Louisiana State University
Topological Data Analysis and The Persistent Laplacian
In this talk, we will go through some basic information about Topological Data Analysis (TDA) such as Persistent Homology with the goal of getting to the Persistent Laplacian and how these tools are used to analyze data.
Posted February 10, 2025
Last modified April 14, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Joshua Mundinger, University of Wisconsin
Hochschild homology of algebraic varieties in characteristic p
Hochschild homology is an invariant of noncommutative rings. When applied to a commutative ring, the Hochschild-Kostant-Rosenberg theorem gives a formula for Hochschild homology in terms of differential forms. This formula extends to the Hochschild-Kostant-Rosenberg decomposition for complex algebraic varieties. In this talk, we quantitatively explain the failure of this decomposition in positive characteristic.
Posted March 25, 2025
Last modified April 20, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:20 pm Lockett 232
Robert Lipton, Mathematics Department, LSU
Dynamic Fast Crack Growth
Nonlocal modeleling for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. The material displacement field is uniquely determined by the initial boundary value problem. The theory naturally satisfies energy balance, with positive energy dissipation rate in accord with the Clausius-Duhem inequality. Notably, these properties are not imposed but follow directly from the constitutive law and evolution equation. The limit of vanishing non-locality is analyzed using simple arguments from geometric measure theory to identify the limit damage energy and weak convergence methods of pde to identify the limit solution. The limiting energy is the Griffith fracture energy. The limit evolution is seen to be a weak solution for the wave equation on a time dependent domain. The existence theory for such solutions was recently developed in Dal Maso and Toader, J. Differ. Equ. 266, 3209–3246 (2019).
Posted April 14, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Qing Zhang, University of California Santa Barbara
Realizing Modular Data from Centers of Near-Group Categories
In this talk, I will discuss modular data arising from the Drinfeld centers of near-group categories. The existence of near-group categories of type $G+n$ can be established by solving a set of polynomial equations introduced by Izumi; a different set of equations, also due to Izumi, can then be used to compute the modular data of their Drinfeld centers. Smaller-rank modular categories can often be obtained from these centers via factorization and condensation. After introducing the background of this framework, I will show the existence of a near-group category of type $\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}/4\mathbb{Z} + 16$ and explain how the modular data of its Drinfeld center can be computed. I will then show that modular data of rank 10 can be obtained via condensation of its Drinfeld center and present an alternative realization of this data through the Drinfeld center of a fusion category of rank 4. Finally, I will discuss the modular data of the Drinfeld center of a near-group category of type $\mathbb{Z}/8\mathbb{Z} + 8$ and demonstrate that the non-pointed factor of its condensation coincides with the modular data of the quantum group category $C(g_2, 4)$. This talk is based on joint work with Zhiqiang Yu.
Posted February 3, 2025
Last modified April 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Nilangshu Bhattacharyya, Louisiana State University
Proof of h-cobordism, Whitney trick and issues in the 4 dimension.
In this presentation, I will begin by recapping the complete proof of the h-cobordism theorem, which states that in dimensions greater than four, a homotopically trivial, simply connected cobordism between two simply connected compact manifolds is smoothly trivial. As a corollary, this implies the higher-dimensional Poincaré conjecture. A central tool in the proof is the Whitney trick, which is effective in higher dimensions. However, in dimension four, a framing obstruction naturally arises, presenting significant challenges. In the latter part of the presentation, I will discuss some of the technical aspects and difficulties associated with applying the Whitney trick.
Posted April 21, 2025
3:30 pm – 4:30 pm Lockett 138
Christopher Kees, Louisiana State University
Application of CutFEM to the modeling of coastal processes through vegetation
Understanding the effects of sea level rise on coastal ecosystems involves complex solid materials, such as mixed sediments and vegetation. Physical flume and basin studies have long been used in coastal engineering to understand wave and current dynamics around such structures. Numerical flumes based on computational fluid dynamics and fluid-structure interaction have recently begun to augment physical models for design studies, particularly for engineered structures where established Arbitrary Lagrangian-Eulerian (ALE) methods based on boundary-conforming meshes and isoparametric or isogeoemtric finite element methods are effective. The rapid growth of lidar and photogrammetry techniques at large scales and computed tomography at small scales has introduced the possibility of constructing numerical experiments for the complex natural materials in coastal ecosystems. These methods tend to produce low-order geometric representations with uneven resolution, which are typically not appropriate for conforming mesh generation. To address this challenge, recent work [1] extended an existing ALE method to include embedded solid dynamics using a piecewise linear CutFEM approach [2]. The implementation is based on equivalent polynomials [3]. The approach retains the convergence properties of the CutFEM method while having a simple implementation within the existing twophase RANS model, which has been used frequently for numerical flume studies. This presentation will consider application and performance of the method for two critical coastal processes: wave interaction with vegetation and sediment dynamics.
Posted January 10, 2025
Last modified March 26, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Carolyn Beck, University of Illinois Urbana-Champaign
IEEE Fellow
Discrete State System Identification: An Overview and Error Bounds
Classic system identification methods focus on identifying continuous-valued dynamical systems from input-output data, where the main analysis of such approaches largely focuses on asymptotic convergence of the estimated models to the true models, i.e., consistency properties. More recent identification approaches have focused on sample complexity properties, i.e., how much data is needed to achieve an acceptable model approximation. In this talk I will give a brief overview of classical methods and then discuss more recent data-driven methods for modeling continuous-valued linear systems and discrete-valued dynamical systems evolving over networks. Examples of the latter systems include the spread of viruses and diseases over human contact networks, the propagation of ideas and misinformation over social networks, and the spread of financial default risk between banking and economic institutions. In many of these systems, data may be widely available, but approaches to identify relevant mathematical models, including underlying network topologies, are not widely established or agreed upon. We will discuss the problem of modeling discrete-valued, discrete-time dynamical systems evolving over networks, and outline analysis results under maximum likelihood identification approaches that guarantee consistency conditions and sample complexity bounds. Applications to the aforementioned examples will be further discussed as time allows.
Posted April 21, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Songling Shan, Auburn University
Linear arboricity of graphs with large minimum degree
In 1980, Akiyama, Exoo, and Harary conjectured that any graph $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests. We confirm the conjecture for sufficiently large graphs with large minimum degree. Precisely, we show that for any given $0<\varepsilon<1$, there exists $n_0 \in \mathbb{N}$ for which the following statement holds: If $G$ is a graph on $n\ge n_0$ vertices of minimum degree at least $(1+\varepsilon)n/2$, then $G$ can be decomposed into at most $\lceil(\Delta(G)+1)/2\rceil$ linear forests. This is joint work with Yuping Gao.
Posted December 10, 2024
Last modified April 27, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Yuanzhen Shao, University of Alabama
Some recent developments in the study of magnetoviscoelastic fluids
In this talk, we consider the motion of a magnetoviscoelastic fluid in a nonisothermal environment. When the deformation tensor field is governed by a regularized transport equation, the motion of the fluid can be described by a quasilinear parabolic system. We will establish the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Further, we will show that that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria. If time permits, we will discuss some recent advancements regarding the scenario where the deformation tensor is modeled by a transport equation. In particular, we will discuss the local existence and uniqueness of a strong solution as well as global existence for small initial data.
Posted April 16, 2025
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Andrew Riesen, MIT
Orbifolds of Pointed Vertex Algebras
We will discuss the interplay of tensor categories $C$ with some group action $G$ and orbifolds $V^G$ of vertex operator algebras (VOAs for short). More specifically, we will show how the categorical structure of $\mathrm{TwMod}_G V$ allows one to not only simplify previous results done purely through VOA techniques but vastly extend them. One such example is the Dijkgraaf-Witten conjecture, now a theorem, which describes how the category of modules of a holomorphic orbifold should look like. Additionally, our techniques also allow us to expand the modular fusion categories known to arise from VOAs, we show that every group-theoretical fusion category comes from a VOA orbifold. This talk is based on joint work with Terry Gannon.
Posted January 12, 2025
Last modified April 29, 2025
Zi Li Lim, UCLA
Rational function progressions
Szemeredi proved that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions. Subsequently, Szemeredi's theorem was generalized to the polynomial and multidimensional settings. We will discuss finding the progressions involving rational functions via Fourier analysis and algebraic geometry.
Posted January 23, 2025
Last modified April 29, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Annette Karrer, The Ohio State University
Connected Components in Morse boundaries of right-angled Coxeter groups
Every finitely generated group G has an associated topological space, called a Morse boundary, that captures the hyperbolic-like behavior of G at infinity. It was introduced by Cordes generalizing the contracting boundary invented by Charney--Sultan. In this talk, we study subgroups arising from connected components in Morse boundaries of right-angled Coxeter groups and of such that are quasi-isom
Posted April 7, 2025
Last modified April 21, 2025
Mark Ellingham, Vanderbilt University
Twisted duality for graph embeddings and conditions for orientability and bipartiteness
*Twisted duals* of embeddings of graphs in surfaces were introduced by Ellis-Monaghan and Moffatt in 2012. They generalize edge twists, well known since the representation of embeddings using rotation schemes and edge signatures was introduced in the 1970s, and partial duals, defined by Chmutov in 2009. I will explain how twisted duals can be found using combinatorial representations of an embedding known as the *gem* (graph-encoded map) and *jewel*. Several important properties of embedded graphs are linked to parity conditions for closed walks in the gem or jewel, and to orientations of the half-edges of the medial graph of the embedding. Using these conditions, I will discuss how we can characterize which twisted duals are orientable or bipartite. This is joint work with Blake Dunshee.
Posted January 16, 2025
Last modified April 5, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Bahman Gharesifard, Queen's University
Structural Average Controllability of Ensembles
In ensemble control, the goal is to steer a parametrized collection of independent systems using a single control input. A key technical challenge arises from the fact that this control input must be designed without relying on the specific parameters of the individual systems. Broadly speaking, as the space of possible system parameters grows, so does the size and diversity of the ensemble — making it increasingly difficult to control all members simultaneously. In fact, an important result among the recent advances on this topic states that when the underlying parameterization spaces are multidimensional, real-analytic linear ensemble systems are not L^p-controllable for p>=2. Therefore, one has to relax the notion of controllability and seek more flexible controllability characteristics. In this talk, I consider continuum ensembles of linear time-invariant control systems with single inputs, featuring a sparsity pattern, and study structural average controllability as a relaxation of structural ensemble controllability. I then provide a necessary and sufficient condition for a sparsity pattern to be structurally average controllable.
Posted April 18, 2025
Combinatorics Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 233 (Simulcast via Zoom)
Mark Ellingham, Vanderbilt University
Maximum genus directed embeddings of digraphs
In topological graph theory we often want to find embeddings of a given connected graph with minimum genus, so that the underlying compact surface of the embedding is as simple as possible. If we restrict ourselves to cellular embeddings, where all faces are homeomorphic to disks, then it is also of interest to find embeddings with maximum genus. For undirected graphs this is a very well-solved problem. For digraphs we can consider directed embeddings, where each face is bounded by a directed walk in the digraph. The maximum genus problem for digraphs is related to self-assembly problems for models of graphs built from DNA or polypeptides. Previous work by other people determined the maximum genus for the very special case of regular tournaments, and in some cases of directed 4-regular graphs the maximum genus can be found using an algorithm for the representable delta-matroid parity problem. We describe some recent work, joint with Joanna Ellis-Monaghan of the University of Amsterdam, where we have solved the maximum directed genus problem in some reasonably general situations.
Posted February 19, 2025
Last modified April 24, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Nina Amini, Laboratory of Signals and Systems, CentraleSupélec
Feedback Control of Open Quantum Systems
First, we provide an overview of control strategies for open quantum systems, that is, quantum systems interacting with an environment. This interaction leads to a loss of information to the environment, a phenomenon commonly referred to as decoherence. One of the principal challenges in controlling open quantum systems is compensating for decoherence. To address robustness issues, feedback control methods are considered. Secondly, we consider the feedback stabilization of open quantum systems under repeated indirect measurements, where the evolution is described by quantum trajectories. I will present our recent results concerning the asymptotic behavior, convergence speed, and stabilization of these trajectories.
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Topology
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Analysis
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Algebra
Posted January 19, 2025
1:00 pm – 4:00 pm Lockett 232Qualifier Exam in Applied Math
Posted March 28, 2025
Last modified April 15, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm TBA
Wenxiong Chen , Yeshiva University
TBA
Posted March 16, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm TBATBA