Calendar
Posted March 19, 2026
Probability Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 276
Aditya Guntuboyina, University of California, Berkeley
What functions does XGBoost learn?
XGBoost is a scalable tree boosting system that is widely used by data scientists for regression. We develop a theoretical framework that explains what kinds of functions XGBoost is able to learn. We introduce an infinite-dimensional function class that extends ensembles of shallow decision trees, along with a natural measure of complexity that generalizes the regularization penalty built into XGBoost. We show that this complexity measure aligns with classical notions of variation—in one dimension it corresponds to total variation, and in higher dimensions it is closely tied to a well-known concept called Hardy–Krause variation. We prove that the best least-squares estimator within this class can always be represented using a finite number of trees, and that it achieves a nearly optimal statistical rate of convergence, avoiding the usual curse of dimensionality. Our work provides the first rigorous description of the function space that underlies XGBoost, clarifies its relationship to classical ideas in nonparametric estimation, and highlights an open question: does the actual XGBoost algorithm itself achieve these optimal guarantees? This is joint work with Dohyeong Ki at UC Berkeley.
Posted March 19, 2026
1:30 pm – 2:30 pm Lockett 276
Aditya Guntuboyina, University of California, Berkeley
What functions does XGBoost learn?
XGBoost is a scalable tree boosting system that is widely used by data scientists for regression. We develop a theoretical framework that explains what kinds of functions XGBoost is able to learn. We introduce an infinite-dimensional function class that extends ensembles of shallow decision trees, along with a natural measure of complexity that generalizes the regularization penalty built into XGBoost. We show that this complexity measure aligns with classical notions of variation—in one dimension it corresponds to total variation, and in higher dimensions it is closely tied to a well-known concept called Hardy–Krause variation. We prove that the best least-squares estimator within this class can always be represented using a finite number of trees, and that it achieves a nearly optimal statistical rate of convergence, avoiding the usual curse of dimensionality. Our work provides the first rigorous description of the function space that underlies XGBoost, clarifies its relationship to classical ideas in nonparametric estimation, and highlights an open question: does the actual XGBoost algorithm itself achieve these optimal guarantees? This is joint work with Dohyeong Ki at UC Berkeley.
Posted January 11, 2026
Last modified March 22, 2026
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 233
Zhiyuan Geng, Purdue University
Asymptotics for 2D vector-valued Allen-Cahn minimizers
For the scalar two-phase (elliptic) Allen–Cahn equation, there is a rich literature on the celebrated De Giorgi conjecture, which reveals deep connections between diffuse interfaces and minimal surfaces. On the other hand, for three or more equally preferred phases, a vector-valued order parameter is required, and the resulting diffuse interfaces are expected to resemble weighted minimal partitions. In this talk, I will present recent results on minimizers of a two-dimensional Allen–Cahn system with a multi-well potential. We describe the asymptotic behavior near the junction of three phases by analyzing the blow-up limit, which is a global minimizing solution converging at infinity to a Y-shaped minimal cone. A key ingredient in our approach is the derivation of sharp upper and lower energy bounds via a slicing argument, which allows us to localize the diffuse interface within a small neighborhood of the sharp interface. As a consequence, we obtain a complete classification of global two-dimensional minimizers in terms of their blow-down limits at infinity. This is joint work with Nicholas Alikakos.
Posted November 15, 2025
Last modified March 22, 2026
Algebra and Number Theory Seminar Questions or comments?
1:20 pm – 2:20 pm Lockett 233 or click here to attend on Zoom
Kiran Kedlaya, University of California San Diego
Implementing the hypergeometric trace formula
Given parameters defining a hypergeometric motive, the trace is given by a rather explicit formula which can be written either in terms of Gauss sums (Beukers–Cohen–Mellit) or, thanks to the Gross–Koblitz formula, the Morita p-adic Gamma function (Cohen–Rodriguez Villegas–Watkins). We explain some of the process of turning this formula into an efficient algorithm "at scale", including an adaptation to compute Frobenius traces in "average polynomial time" in the sense of David Harvey's recent Arizona Winter School lectures; that part is joint with Edgar Costa and David Harvey.
Event contact: Hasan Saad and Gene Kopp
Posted March 17, 2026
Last modified March 22, 2026
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Ian Jorquera, Colorado State University
Switching equivalence of systems of lines over finite fields
In this talk we will discuss important frame theoretic objects such at equiangular tight frames (ETFs) whose existence has important applications in fields as diverse as compressed sensing to quantum state tomography. We will then discuss some new approaches to tackling some open problems, on the existence and structure of these frame theoretic objects, by using tools from geometric algebra, and specially looking at frames over finite field vector spaces with Hermitian forms. We will then show that the switching equivalence classes of systems of lines over finite fields which are frames, often only depend on the double and triple products. This allows us to understand ETFs over finite fields in terms of their double and triple products, with a result similar to saturating the Welch bound over $\mathbb{C}$. We also show that similar to the case over $\mathbb{C}$, collections of vectors are similar to a regular simplex essentially when their triple products satisfy a certain property.
Event contact: Gene Kopp
Posted March 14, 2026
3:30 pm – 4:30 pm Lockett 239
Aditya Guntuboyina, University of California, Berkeley
Totally Concave Regression
We provide a general overview of regression under concavity shape constraints. In the multivariate setting, several notions of concavity exist, each with substantially different properties. We review these variants and highlight their key differences. Our main focus is on an approach based on total concavity, originally studied by T. Popoviciu, which avoids the usual curse of dimensionality and can be effective in practical applications.
Posted March 11, 2026
Computational Mathematics Seminar
3:30 pm – 4:30 pm Digital Media Center 1034
Yanzhao Cao, Auburn University
A training-free diffusion model for generative learning
Abstract: In this talk, I will first present a framework for training generative models for density estimation using stochastic differential equations (SDEs). Unlike conventional diffusion models that train neural networks to learn the score function, we introduce a score-estimation method that is training-free. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatiotemporal location while solving the ordinary differential equation (ODE) corresponding to the reverse-time SDE. Our method provides high accuracy and significant reductions in neural network training time. Algorithm development and convergence analysis will be discussed. At the end, I will present an application of the diffusion model to fusion plasma.
Posted March 9, 2026
Last modified March 20, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Zhiwei Wang, Louisiana State University
Some recent progress on frequency methods to quantitative unique continuation
We study quantitative unique continuation for elliptic equations with lower order terms of H\"older regularity via a frequency function method. We establish quantitative three-ball inequalities and corresponding vanishing-order bounds. Our results are quantitative with explicit dependence of the three-ball constants and the vanishing-order exponents on the H\"older exponent, which has a unified framework matching sharp endpoint results.
Posted March 3, 2026
Last modified March 9, 2026
Shuang Guan, Tufts University
The HRT Conjecture for a Symmetric (3,2) Configuration
The Heil-Ramanathan-Topiwala (HRT) conjecture is an open problem in time-frequency analysis. It asserts that any finite combination of time-frequency shifts of a non-zero function in $L^2(\mathbb{R})$ is linearly independent. Despite its simplicity, the conjecture remains unproven in full generality, with only specific cases resolved. In this talk, I will discuss the HRT conjecture for a specific symmetric configuration of five points in the time-frequency plane, known as the (3,2) configuration. We prove that for this specific setting, the Gabor system is linearly independent whenever the parameters satisfy certain rationality conditions (specifically, when one parameter is irrational and the other is rational). This result partially resolves the remaining open cases for such configurations. I will outline the proof methods, which involve an interplay of harmonic analysis and ergodic theory. This is joint work with Kasso A. Okoudjou.
Posted January 15, 2026
Last modified March 23, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Saumya Jain, Louisiana State University
Right-angled Mock Reflection Groups
Right-angled Coxeter groups (RACGs) and certain groups arising from blow-ups act isometrically on CAT(0) cube complexes in a reflection-like manner. Right-angled mock reflection groups (RAMRGs) generalize this class of groups. In this talk, I will introduce RAMRGs and explain how their group structure can be encoded combinatorially using graphs with additional local data. We will also discuss examples and see a characterization of all finite RAMRGs.
Posted January 15, 2026
Last modified March 23, 2026
Colloquium Questions or comments?
3:30 pm Lockett 232
Kumar Murty, University of Toronto
Non-vanishing of Poincare series
A famous conjecture of Lehmer asserts that there is no positive integer n for which the Ramanujan function tau(n) vanishes. This has been verified numerically for n up to a very large bound, but a general proof still eludes us. In this talk, we view this conjecture in terms of the non-vanishing of a family of cusp forms called Poincare series. We introduce a new method by which it is possible to prove the non-vanishing of many of these cusp forms.
Posted January 5, 2026
Last modified March 9, 2026
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Zoom (click here to join)
Jonathan How, Massachusetts Institute of Technology
AIAA and IEEE Fellow
Resilient Multi-Agent Autonomy: Perception and Planning for Dynamic, Unknown Environments
Unmanned ground and aerial systems hold promise for critical applications, including search and rescue, environmental monitoring, and autonomous delivery. Real-world deployment in safety-critical settings, however, remains challenging due to GPS-denied operation, perceptual uncertainty, and the need for safe trajectory planning in dynamic unknown environments. This talk presents recent advances in planning, control, and perception that together enable robust, scalable, and efficient aerial autonomy. On the planning and control side, I first introduce DYNUS, which enables uncertainty-aware trajectory planning for safe, real-time flight in dynamic and unknown environments. Building on this foundation, MIGHTY performs fully coupled spatiotemporal optimization to generate agile and precise motion by jointly reasoning about path and timing. Together with prior work on Robust MADER, these methods enable fast, safe, multi-robot navigation under uncertainty. On the perception side, I introduce complementary mapping frameworks that support long-term autonomy and planning. GRAND SLAM combines 3D Gaussian splatting with semantic and geometric priors to produce unified scene representations suitable for photorealistic planning. A second example is ROMAN, which builds on ideas from our prior open set mapping work including SOS MATCH and VISTA. ROMAN compresses environments into sparse, object-centric maps that are orders of magnitude smaller than traditional representations, while still enabling accurate re-localization and loop closure under extreme viewpoint changes. I also discuss the interaction between perception and control, with a focus on safety filtering for systems that rely on learned perception models. Finally, I present results from simulation and hardware experiments and conclude with open challenges in building resilient autonomous aerial systems. Together, these advances move us closer to reliable multi-robot autonomy with meaningful real-world impact. [For the speaker's biographical sketch, click here.]
Posted January 2, 2026
Last modified March 11, 2026
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Joint Computational Mathematics and Control and Optimization Seminar to Be Held In Person in 233 Lockett Hall and on Zoom (click here to join)
Jia-Jie Zhu, KTH Royal Institute of Technology in Stockholm
Optimization in Probability Space: PDE Gradient Flows for Sampling and Inference
Many problems in machine learning and Bayesian statistics can be framed as optimization problems that minimize the relative entropy between two probability measures. In recent works, researchers have exploited the connection between the (Otto-)Wasserstein gradient flow of the Kullback-Leibler (or KL) divergence and various sampling and inference algorithms, interacting particle systems, and generative models. In this talk, I will first contrast the Wasserstein flow with the Fisher-Rao flows of a few entropy energy functionals, and showcase their distinct analysis properties when working with different relative entropy driving energies, including the reverse and forward KL divergence. Building upon recent advances in the mathematical foundation of the Hellinger-Kantorovich (HK, a.k.a. Wasserstein-Fisher-Rao) gradient flows, I will then show the analysis of the HK flows and its implications in examples of machine learning tasks.
Event contact: Susanne Brenner
Posted March 26, 2026
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 (Simulcast via Zoom)
James "Dylan" Douthitt, Syracuse University
M is for Matroids
Kennard, Wiemeler, and Wilking established a relationship between torus representations with connected isotropy group and regular matroids. In this talk, I will discuss reproving some of their main results using matroid theoretic techniques. Further, we strengthen these results by showing the invariants used are equal irrespective of the object being cocircuits or disjoint unions of circuits. This talk is based on joint work with Elana Israel and Lee Kennard.
Posted March 30, 2026
Probability Seminar Questions or comments?
12:00 pm – 1:00 pm Lockett 243
Olga Iziumtseva, University of Nottingham
Self-intersection local times of Volterra Gaussian processes in stochastic flows with interaction
In this talk, we discuss the existence of multiple self-intersection local times for stochastic processes $x(u(s),t), s\in [0,1]$, where $u$ is a Volterra Gaussian process and $x$ is the solution to the equation with interaction driven by the occupation measure of the process $u$. It appears that self-intersection local times for the process $x(u(s),t), s\in[0,1]$ can be defined as weighted self-intersection local times for the process $u$. We present conditions on Volterra Gaussian processes and weight functions sufficient for the existence of weighted self-intersection local times for a large class of unbounded weights. This is a joint work with Wasiur R. Khudabukhsh
Posted March 27, 2026
Last modified March 30, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Jai Tushar, Louisiana State University
Polytopal finite element methods
Many problems in science and engineering are modelled by partial differential equations, but solutions are often impossible to compute analytically. One of the most successful tools to numerically approximate such solutions of such problems in one, two and three spatial dimensions are the Finite Element Methods (FEMs). FEM approximates the unknown solution over the domain by subdividing the domain into smaller, simpler pieces called finite element. Traditionally these pieces are simple shapes such as triangles/tetrahedra or quadrilaterals/hexahedra. But in many applications, it is useful to allow more general shapes. In this talk, I will give an informal introduction to the design and analysis of polytopal FEMs, where the computational mesh is made of general polytogonal/polyhedral elements.
Posted January 15, 2026
Last modified March 30, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
An odd Khovanov stable homotopy type
Khovanov homology admits two integral variants: the original (“even”) theory and the Ozsváth–Rasmussen–Szabó (“odd”) refinement. While both categorify the Jones polynomial and agree over \mathbb{F}_2, their algebraic structures differ in subtle ways. In this talk, I will survey homotopy-theoretic refinements of Khovanov homology, focusing on the Lipshitz–Sarkar stable homotopy type and its odd analogue. I will explain how these spectra are constructed from Burnside categories and homotopy colimits, compare key structural features of the even and odd theories, and discuss their relationship.
Posted March 1, 2026
Last modified March 26, 2026
Simon Bortz, University of Alabama
Parabolic Quantitative Rectifiability, Singular Integrals, and PDEs
I will discuss the origins of quantitative rectifiability, starting with the Littlewood–Paley g-function and the Fefferman–Stein characterization of BMO via Poisson extensions. From this point of view, I will describe some of the motivations behind the David–Semmes characterization of uniform rectifiability in terms of Jones’ $L^2$ beta numbers. I will then discuss my work establishing parabolic analogues of some of the equivalences proved by David and Semmes in the elliptic setting, as well as related work by others. I will conclude with recent work connecting this theory to the Dirichlet problem for the heat equation and to quantitative properties of caloric functions.
Posted March 17, 2026
Last modified March 30, 2026
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Shahriyar Roshan-Zamir, Tulane University
Interpolation in Weighted Projective Spaces
Over an algebraically closed field, the double point interpolation problem asks for the vector space dimension of the projective hypersurfaces of degree d singular at a given set of points. After being open for 90 years, a series of papers by J. Alexander and A. Hirschowitz in 1992--1995 settled this question in what is referred to as the Alexander-Hirschowitz theorem. In this talk, we primarily use commutative algebra to prove analogous statements in the weighted projective space, a natural generalization of the projective space. For example, we introduce an inductive procedure for weighted projective space, similar to that originally due to A. Terracini from 1915, to demonstrate an example of a weighted projective plane where the analogue of the Alexander-Hirschowitz theorem holds without exceptions and prove our example is the only such plane. Furthermore, Terracini's lemma regarding secant varieties is adapted to give an interpolation bound for an infinite family of weighted projective planes. There are no prerequisites for this talk besides some elementary knowledge of algebra.
Event contact: Gene Kopp
Posted March 27, 2026
Last modified April 5, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Yixing Miao, Louisiana State University
Spectra of Magnetic Schrodinger Operators on Hexagonal Graph
In this presentation, I will talk about my ongoing work on the spectral analysis of Hamiltonians defined on the hexagonal graph with delta-like interactions, which is a generalization of previous work by Becker, Han, and Jitomirskaya. The methodology is to reduce the study of spectra of Hamiltonians to that of quasi-periodic Jacobi operators. The main difficulty is due to the parameters of we introduced in the delta-like boundary conditions. It requires us to modify the proofs of several theorems related to the spectral analysis of quasi-periodic Jacobi operators, and results in various spectral types dependent on those parameters. Numerous tools from ODE, Fourier analysis, functional analysis, complex analysis, dynamical systems, etc... are involved.
Posted January 15, 2026
Last modified April 7, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Spanning tree complex and Khovanov homology
This talk will give an introduction to the spanning tree model for Khovanov homology. Starting from a knot or link diagram, one can associate a planar graph by checkerboard coloring, and the spanning trees of this graph turn out to capture an important part of the structure of the Khovanov complex. I will explain how this viewpoint leads to a simpler complex generated by spanning trees, why it is natural from the perspective of the Jones polynomial, and how it helps illuminate the combinatorial structure underlying Khovanov homology. The emphasis will be on the main ideas and examples, with the goal of making the spanning tree complex accessible to a broad audience.
Posted April 7, 2026
Probability Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett 138
Wasiur KhudaBukhsh, University of Nottingham
A probabilistic view on perturbations of the identity operator
Perturbation analysis of operators is a classical topic in functional analysis. In this talk, we will look at perturbations of the identity operator from a probabilistic perspective in which the identity operator corresponds to the Wiener process. It is well known that the three functionals of the Wiener trajectories, namely, the time of the maxima, the amount of time spent in the positive half of the real line, and the time of the last zero, follow the arcsine law. We provide an elementary proof of the universality of the arcsine laws when the identity operator is perturbed by an absolutely continuous operator in $L_2([0, 1])$.
Posted March 20, 2026
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Louisana Digital Media Center
Tan Bui-Thanh, The University of Texas at Austin
Professor and the Endowed William J. Murray, Jr. Fellow in Engineering
Rigorous Model-Constrained Scientific Machine Learning for Digital Twins: A Computational Mathematics Perspective
Digital twins (DTs) are high-fidelity virtual representations of physical systems and processes. At their foundation lie mathematical and physical models that describe system behavior across multiple spatial and temporal scales. A central purpose of DTs is to enable "what-if" analyses through hypothetical simulations, supporting lifecycle monitoring, parameter calibration against observational data, and systematic uncertainty quantification (UQ). For DTs to serve as a reliable basis for real-time forecasting, optimization, and decision-making, they must reconcile two traditionally competing requirements: mathematical rigor and physical fidelity, and computational efficiency at scale. This has motivated a new generation of approaches that combine classical tools from numerical analysis, partial differential equations, inverse problems, and optimization with the expressive power of Scientific Machine Learning (SciML). In this talk, I will outline a principled pathway from traditional computational mathematics to rigorously grounded SciML. I will then present recent Scientific Deep Learning (SciDL) methods for forward modeling, inverse and calibration problems, and uncertainty quantification, emphasizing mathematical structure, stability, and generalization. Both theoretical results and numerical demonstrations will be shown for representative problems governed by transport, heat, Burgers, Euler (including transonic and hypersonic regimes), and Navier- Stokes equations.
Event contact: Robert Lipton
Posted February 5, 2026
Last modified February 6, 2026
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Zoom (click here to join)
Wonjun Lee, Ohio State University
Linear Separability in Contrastive Learning via Neural Training Dynamics
The SimCLR method for contrastive learning of invariant visual representations has become extensively used in supervised, semi-supervised, and unsupervised settings, due to its ability to uncover patterns and structures in image data that are not directly present in the pixel representations. However, this success is still not well understood; neither the loss function nor invariance alone explains it. In this talk, I present a mathematical analysis that clarifies how the geometry of the learned latent distribution arises from SimCLR. Despite the nonconvex SimCLR loss and the presence of many undesirable local minimizers, I show that the training dynamics driven by gradient flow tend toward favorable representations. In particular, early training induces clustering in feature space. Under a structural assumption on the neural network, our main theorem proves that the learned features become linearly separable with respect to the ground-truth labels. To support the theoretical insights, I present numerical results that align with the theoretical predictions.
Posted March 27, 2026
Last modified April 6, 2026
Geometry and Topology Seminar Seminar website
1:30 pm Lockett 233
Chris Manon, University of Kentucky
Toric tropical vector bundles
A toric vector bundle is a vector bundle over a toric variety which is equipped with a lift of the action action of the associated torus. As a source of examples, toric vector bundles and their projectivizations provide a rich class of spaces that still manage to admit a combinatorial characterization. Toric vector bundles were first classified by Kaneyama, and later by Klyachko using the data of decorated subspace arrangements. Klyachko's classification is the foundation of many interesting results on toric vector bundles and has recently led to a connection between toric vector bundles, matroids, and tropical geometry. After explaining some of this background, I'll introduce the notion of a tropical toric vector bundle over a toric variety. These objects are discrete analogues of vector bundles which still have notions of positivity, a sheaf of sections, an Euler characteristic, and Chern classes. The combinatorics of these invariants can reveal properties of their classical analogues as well as point the way to new theorems for tropical vector bundles over a more general base. Time permitting, I will discuss some new results on higher Betti numbers of a tropical vector bundle.
Posted April 8, 2026
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (Click here to join)
Tong Jin, Vanderbilt University
Representation theory of orthogonal matroids.
Orthogonal matroids generalize maximal isotropic spaces just as matroids generalize linear spaces, and they are Coxeter matroids of type D_n in the sense of Borovik--Gelfand--White, and even \Delta-matroids or tight 2-matroids in the sense of Bouchet. In this talk, we construct the foundation F_M of an orthogonal matroid M, which processes the universal property that the set of equivalence classes of representations of M over a field F is naturally in one-to-one correspondence with Hom(F_M, F). We also give an explicit presentation of the foundation F_M as an algebra over the regular partial field. The presentation here has a different set of generators from the matroid case in the work of Baker--Lorscheid, and a central theorem in this approach is a new characterization of representations of orthogonal matroids by circuits. We end this talk with some interesting examples of foundations of orthogonal matroids that are representable over all fields, and we will see phenomena that don’t appear in matroids.
Posted February 9, 2026
Last modified March 9, 2026
Michael Kurtz, ExxonMobil
Industry Speaker
Motivation for, Challenges to, and Progress in the Use of Advanced Data Science Methodologies for Improved Chemical Manufacturing
Event contact: Maganizo Kapita, Laura Kurtz
Posted April 8, 2026
Last modified April 12, 2026
Informal Analysis Seminar Questions or comments?
12:30 pm – 1:30 pm Lockett 233
Arif Ali, Louisiana State University
Introduction to Girsanov's Theorem and Some Application
In this talk, we introduce Girsanov’s Theorem. This theorem is an important result in stochastic calculus that describes how probability measures can be changed to alter the drift of a Brownian motion. After briefly reviewing some concepts from stochastic analysis, we present the theorem and its proof. Then we show how Girsanov’s Theorem can be applied to remove drift from a stochastic process and simplify stochastic differential equations, illustrating its central role in the analysis of SDEs.
Posted January 15, 2026
Last modified April 12, 2026
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett Hall 233
Anurakti Gupta, Louisiana State University
Transverse knots distinguished by Knot Floer Homology
I will discuss a paper by Lenhard Ng, Peter Ozsváth, and Dylan Thurston, in which they use knot Floer homology to distinguish transverse knots. In particular, they show that transverse knots with the same self-linking number need not be transversely isotopic. I will describe the invariant using the combinatorial construction of knot Floer homology with coefficients in F_2.
Posted March 9, 2026
Last modified April 6, 2026
Alexander Burgin, Georgia Tech
Integer Cantor sets: Harmonic-analytic properties & arithmetic applications.
Integer Cantor sets, which consist of a set of integers in a fixed base and a fixed set of digits, have many interesting properties, including uniform distribution, metric pair correlation, and mean ergodic theorems. In particular, their Fourier transform factorizes. I’ll begin with a motivation from ergodic theory, and proceed to discuss some recent results of myself, Fragkos, Lacey, Mena, and Reguera. If time permits, I will discuss some arithmetic applications of these estimates.
Posted December 27, 2025
Last modified April 11, 2026
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Zoom (click here to join)
Aris Daniilidis, Technische Universität Wien
Variational Stability of Alternating Projections
The alternate projection method is a classical approach to deal with the convex feasibility problem. We shall first show that given two nonempty closed convex sets $A$ and $B$, the consecutive projections $x_{n+1} = P_B(P_A(x_n))$, $n \ge 1$ produce a self-contacted sequence, providing in particular an alternative way to establish convergence in the finite dimensional case [2]. In infinite dimensions, a regularity condition is required to ensure convergence of the above sequence $\{x_n\}_{n\ge 1}$ [4]. In [3], it was established that a regularity condition from [1] also ensures the variational stability of the above method. In this talk, we shall complete this result and show that variational stability is actually equivalent to the aforementioned regularity assumption. REFERENCES: [1] H. Bauschke, J. Borwein, On the convergence of von Neumann’s alternating projection algorithm for two sets, Set-Valued Anal. 1 (1993), 185–212. [2] A. Bohm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128. [3] C. De Bernardi, E. Miglierina, A variational approach to the alternating projections method, J. Global Optim. 81 (2021), 323-350. [4] H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (2004), 35–61.
Posted April 11, 2026
LSU AWM Student Chapter LSU AWM Student Chapter Website
12:30 pm Keisler LoungeAWM Officer Elections
AWM will be holding our annual officer elections for the academic year 2026-27. Any present LSU AWM member will be able to vote, with membership sign-up available day-of. Register to run with our officer candidate form. We're excited to meet the candidates! All are welcome! Don't hesitate to reach out if you have any questions.
Event contact: jgarc86@lsu.edu
Posted April 13, 2026
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 (Simulcast via Zoom)
Gyaneshwar Agrahari, LSU
Counting $K_{1,t}$ and $K_{2,t}$ in higher connected triangulations
In 1979, Hakimi and Schmeichel initiated the study of the maximum number of copies of a fixed subgraph in planar graphs by determining the maximum number of \( C_3 \) and \( C_4 \) in an \( n \)-vertex planar graph. In 1984, Alon and Caro determined the maximum numbers of copies of $K_{1,t}$ and $K_{2,t}$ in an $n$-vertex planar triangulation. Throughout the years, graph theorists have solved similar problems for longer cycles, including Hamiltonian cycles, paths, and other subgraphs. In the case of Hamiltonian cycles, there are at least quadratically many Hamiltonian cycles in a 4-connected planar triangulation. However, in a 5-connected $n$-vertex planar triangulation, there are exponentially many Hamiltonian cycles, proving that connectivity can play a significant role in enumerating certain subgraphs. We determine the exact maximum number of copies of $K_{1,t}$ and $K_{2,t} $ in a $4$-connected planar triangulation, and that of $K_{1,t}$ in a $5$-connected planar triangulation. We also characterize all extremal graphs that attain these bounds.
Posted April 20, 2026
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Shilin Lai, University of Michigan
Euler system test vectors and relative Satake isomorphism
The construction of Euler systems often involves delicate choices of local test vectors. Using the relative Satake isomorphism, in particular the unramified Plancherel formula, we give a conceptual proof of their existence in many settings. As an example, we will treat the Gan–Gross–Prasad and Friedberg–Jacquet case uniformly. This is joint work with Li Cai and Yangyu Fan.
Event contact: Joseph DiCapua and Gene Kopp