Calendar
Posted March 16, 2025
Last modified October 5, 2025
Applied Analysis Seminar Questions or comments?
2:30 pm Lockett 233
Nicola Garofalo, Arizona State University
Charles Wexler Professor in Mathematics,
Strichartz estimates for degenerate dispersive equations
I will discuss some new Ginibre-Velo estimates for a class of Schrodinger equations with a possibly strongly degenerate Hamiltonian. The talk will have a self-contained character and I will focus on some interesting examples
Event contact: Phuc/Zhu
Posted August 3, 2025
Last modified October 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Donatella Danielli, Arizona State University
School Director and Foundation Professor
Obstacle Problems for Fractional Powers of the Laplacian
In this talk we will discuss a two-penalty boundary obstacle problem for a singular and degenerate elliptic operator naturally arising in the extension procedure for the fractional Laplacian $(-\Delta)^s$ when s between 1 and 2. Our goals are to establish regularity properties of the solution and the structure of the free boundary. To this end, we combine classical techniques from PDEs and the calculus of variations with more modern methods, such as the localization of the operator and monotonicity formulas. In particular, we will emphasize the striking differences with the cases s between 0 and 1 and s=$3/2$. This is joint work with A. Haj Ali (University of Michigan) and G. Gravina (Loyola University-Chicago).
Event contact: Phuc/Zhu
Posted October 3, 2025
5:00 pm – 6:00 pm Keisler Lounge, Lockett HallGrad School Panel Night
LSU SIAM Student Chapter and the Math Club will be hosting a joint meeting for a Grad School Panel Night. The goal of the event is to inform undergraduate students about the graduate school application process, focusing on topics such as application materials, deadlines, CVs, selecting a suitable graduate school, and transitioning to grad life. If you are a graduate student or a faculty member and would like to share your experience with the undergraduates, feel free to swing by. Food will be provided for in-person attendees.
Event contact: Segolene Ntipouna and Maganizo Kapita
Posted September 30, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm Lockett 233 or click here to attend on Zoom
Jianqi Liu, University of Pennsylvania
Modular invariance of intertwining operators from the factorization theorem of conformal blocks
The notion of conformal blocks on stable curves defined by modules over a vertex operator algebra (VOA) generalizes the WZNW-conformal blocks defined by modules over affine Lie algebras. Recent advances in the theory of VOA-conformal blocks have shed new light on the representation theory of VOAs. In particular, the factorization theorem and the vector bundle property of the sheaves of VOA-conformal blocks lead to the modular invariance of intertwining operators for strongly rational VOAs. In this talk, I will explain the proof of this theorem and present a short proof of the associativity of fusion rings for VOAs. This talk is based on joint work with Xu Gao.
Posted October 7, 2025
Faculty Meeting Questions or comments?
3:00 pm ZoomMeeting of the Tenured Faculty
Posted October 5, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Bart Rozenweig, Ohio State University
Borel Summability in Quantum Theory
Borel summation is a canonical summation technique which associates to a divergent power series an analytic function, for which the power series is its asymptotic expansion. This talk gives an overview of asymptotic expansions and the fundamental results on Borel summability, before surveying two major applications of the theory: first, in building actual solutions out of divergent formal power series solutions of ODEs and PDEs; and second, in making sense of divergent Rayleigh-Schrödinger perturbation expansions in quantum mechanics. Along the way, we will touch upon some key aspects of “resurgence theory”, a paradigm for the application of Borel summation ideas in quantum field theory.
Posted August 27, 2025
Last modified October 4, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted October 7, 2025
Faculty Meeting Questions or comments?
1:30 pm ZoomMeeting of the Tenured Faculty
Posted October 6, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Scott Baldridge, Louisiana State University
How to Build a Toy 2+1 ``Theory of Everything’’ model of the universe in 137 Easy Steps
Can a simple 2D combinatorial model already show us how to fuse matter and geometry into one quantum framework? String Theory (with its background-choice and vacuum-multiplicity issues) and Loop Quantum Gravity (with its dynamical ambiguities) both leave gaps. To keep the talk simple, I stay on a closed 2D surface and use metric triangulations to build a refinement-invariant Penrose polynomial (invariant under 1-3 Pachner refinements) that, under resampling, converges to a smooth metric. This polynomial is then an invariant of the triangulation-refinement class of a Riemannian manifold. I next tie the Penrose polynomial to the Regge action to produce a quantum gravity action whose equations of motion match the Einstein equations of general relativity (in 2D), and I use 2-2 Pachner flips as a ``discrete time step’’ in the toy model to illustrate dynamics. The talk focuses on explicit, easy-to-follow graph constructions and computations suitable for graduate students (and advanced undergraduates). If time, I conclude by outlining how the same blueprint extends to 3D, actual spacetime, where the model becomes genuinely dynamical. Note: The 137 steps is obviously a joke! It’s more like 35 steps, but I’ll only show you a few of them to give you the idea of how it works. Also: This talk is NOT a continuation of last week’s talk. However, the full theory does use aspects of it for those who attended.
Posted October 2, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Wilhelm Schlag, Yale University
On uniqueness of excited states and related questions
This talk will present the long-standing problem of excited states uniqueness for the nonlinear Schroedinger equation. We will describe the history of the problem, it's relevance to long-term dynamics of nonlinear wave equations, related spectral problems, and progress on the uniqueness question via rigorous numerics. The recent breakthrough by Moxun Tang, who found an analytical proof, will be discussed.
Posted August 1, 2025
Last modified October 3, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Felix Schwenninger, University of Twente, The Netherlands
Infinite-Dimensional Input-to-State Stability (ISS) -- Peculiarities of Sup-Norms
E. Sontag’s input-to-state stability (ISS), dating back to the late 80ies, is a cornerstone of modern mathematical control theory. While originally studied for finite-dimensional systems, the theory about infinite-dimensional systems, and in particular models involving partial differential equations, has been developed in the past 15 years. Somewhat surprisingly, the linear case, which is trivial in finite-dimensions, even offered challenges with respect to the mutual relations of several variants of ISS. In this talk we will focus in particular on “integral ISS” for linear and bilinear systems and discuss established results as well as more recent findings. The underlying reason for these subtleties is primarily due to the nontrivial interplay of supremum-norms, which naturally arise in ISS), and the (Banach space) geometry of the state spaces.
Posted October 6, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (click here to join)
Lina Li, University of Mississippi
Lipschitz functions on weak expanders
Given a connected finite graph $G$, an integer-valued function $f$ on $V(G)$ is called $M$-Lipschitz if the value of $f$ changes by at most $M$ along the edges of $G$. In 2013, Peled, Samotij, and Yehudayoff showed that random $M$-Lipschitz functions on graphs with sufficiently good expansion typically exhibit small fluctuations, giving sharp bounds on the typical range of such functions, assuming $M$ is not too large. We prove that the same conclusion holds under a relaxed expansion condition and for larger $M$, (partially) answering questions of Peled et al. Our approach combines Sapozhenko’s graph container method with entropy techniques from information theory. This is joint work with Krueger and Park.
Posted October 3, 2025
Last modified October 8, 2025
A Conversation with SIAM President
The SIAM Student Chapter and AWM Student Chapter are excited to host a Special Q and A session with the President of SIAM. This event provides students with an opportunity to directly engage with the President, ask questions, and gain insights into the world of Applied Mathematics and Computational Science. Refreshments will be provided.
Event contact: Gowri Priya Sunkara and Laura Kurtz
Posted August 2, 2025
Last modified October 8, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kenz Kallal, Princeton University
Algebraic theory of indefinite theta functions
Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature, using the Poisson summation formula. However, $\Theta$ was originally invented by Fourier (Théorie analytique de la chaleur, 1822) for the purpose of studying the diffusion of heat on a uniform circle-shaped material: it is the fundamental solution to the heat equation on a circle. By algebraically characterizing the heat equation as a specific flat connection on a certain bundle on a modular curve, we produce a completely algebraic technique for proving modularity of theta functions. More specifically, we produce a refinement of the algebraic theory of theta functions due to Moret-Bailly, Faltings–Chai, and Candelori. As a consequence of the algebraic nature of our theory and the fact that it applies to indefinite quadratic forms / non-ample line bundles (which the prior algebraic theory does not), we also generalize the Kudla–Millson analytic theory of theta functions for indefinite quadratic forms to the case of torsion coefficients. This is joint work in progress with Akshay Venkatesh.
Posted October 10, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Long Teng, LSU
Nodal Sets of Harmonic Functions
In this talk, we study the size of nodal sets of harmonic functions. We introduce the frequency function N(r), which quantifies the growth rate of a harmonic function and plays a crucial role in understanding its zero set. I will first define this frequency function and show its monotonicity property. Then, using this tool, we establish that the (n−1)-dimensional Hausdorff measure of the nodal set is bounded above by C(n)N, where C(n) depends only on the dimension. This result highlights how quantitative unique continuation connects analytic growth properties of harmonic functions to the geometric complexity of their nodal sets.
Event contact: Laura Kurtz
Posted September 26, 2025
Last modified October 13, 2025
Geometry and Topology Seminar Seminar website
1:30 pm Virtual
Naageswaran Manikandan, Max Planck Institute
Obstructions to positivity notions using Khovanov-type theories.
In this talk, we discuss how Khovanov homology theories can be employed to construct obstructions to various notions of positivity in knot theory. We begin by discussing a result showing that, for a positive link, the first Khovanov homology is supported in a single quantum grading, is free abelian, and its rank reflects whether the link is fibered. We extend these results to (p,q)-cables of positive knots whenever $q \geq p$. We then turn to ongoing work investigating how odd-Khovanov homology and Khovanov-Rozansky homology can be used to construct obstructions to these positivity notions.
Posted August 27, 2025
Last modified October 15, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Adithyan Pandikkadan, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology, follow Melissa Zhang's notes.
Posted September 10, 2025
Last modified October 14, 2025
Bruno Poggi, University of Pittsburgh
The Dirichlet problem as the boundary of the Poisson problem
We review certain classical quantitative estimates (known as non-tangential maximal function estimates) for the solutions to the Dirichlet boundary value problem for the Laplace equation in a smooth domain in Euclidean space, when the boundary data lies in an $L^p$ space, $p>1$. A natural question that arises is: what might an analogous estimate for the inhomogeneous Poisson problem look like? We will answer this question precisely, and in so doing, we will unravel deep and new connections between the solvability of the (homogeneous) Dirichlet problem for the Laplace equation with data in $L^p$ and the solvability of the (inhomogeneous) Poisson problem for the Laplace equation with data in certain Carleson spaces. We employ this theory to solve a 20-year-old problem in the area, to give new characterizations and a new local T1-type theorem for the solvability of the Dirichlet problem under consideration. Some of the new results are the product of joint works with Mihalis Mourgoglou and Xavier Tolsa.
Event contact: Phuc C. Nguyen
Posted October 6, 2025
Last modified October 15, 2025
Mathematical Physics and Representation Theory Seminar
1:30 pm – 2:20 pm Lockett 233
John O'Brien, Louisiana State University
The Splitting-Rank Derived Satake Equivalence
This talk is based on joint work with Tsao-Hsien Chen, Mark Macerato, and David Nadler. We discuss a generalization of Bezrukavnikov-Finkelberg's Derived Satake Equivalence from complex reductive groups to certain real reductive groups--or equivalently, from compact Lie groups to the corresponding symmetric spaces. We use Nadler's Real Geometric Satake to compute the equivariant cohomology of the based loop space of a splitting-rank symmetric space, then use Achar's parity-vanishing machinery to establish the equivalence of derived categories.
Posted August 27, 2025
Last modified October 15, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett Hall 233
Xuenan Li, Columbia University
Soft modes in mechanism-based mechanical metamaterials: modeling, analysis, and applications
Mechanism-based mechanical metamaterials are synthetic materials that exhibit unusual microscale buckling in response to mechanical deformations. These artificial materials are like elastic composites but sometimes more degenerate since they can deform with zero elastic energy. We call such zero energy deformations mechanisms. Origami and Kirigami are typical examples of these mechanism-based mechanical metamaterials. Other than mechanisms, these metamaterials also have "soft modes" -- macroscopic deformations with very little elastic energy, some but not all of which resemble modulated mechanisms. A key question is to identity all the soft modes for a given mechanism-based metamaterial. In this talk, I will address the two-fold challenge in identifying the soft modes and our treatments: first, we establish the existence of an effective energy for a broad class of lattice metamaterials; and second, we identify soft modes as macroscopic deformations where this energy vanishes, including a complete characterization of the zero sets of the effective energy in some conformal metamaterials. Together, these results provide a rigorous link between mechanisms and soft modes, laying a mathematical foundation for future analysis and design of mechanical metamaterials. This is joint work with Robert V. Kohn.
Event contact: Stephen Shipman
Posted September 2, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm Lockett 233 or click here to attend on Zoom
Guanyu Li, Cornell University
Derived Commuting Schemes, Representation Homology, and Cohomology of Lie Algebras
The commuting schemes of an algebraic group or a Lie algebra play important roles in many areas of mathematics. They can be viewed as special cases of representation schemes, which are often highly singular. Derived algebraic geometry provides tools to remedy the deficiency. In particular, the derived representation scheme, together with its associated algebraic invariant known as representation homology, offers deeper insights into the structure of representation schemes. While the representation homology of reductive groups and reductive Lie algebras has been studied in the literature, it is natural to ask about the behavior of these objects and their relationships in the non-reductive setting. In this talk, I will discuss the derived commuting scheme of a maximal unipotent subgroup of a semisimple group scheme, as well as the derived commuting scheme of its Lie algebra. First, the higher structure of the derived commuting scheme detects whether the underlying commuting scheme is a complete intersection. Unlike the reductive case, the derived commuting scheme of a unipotent subgroup is equivalent to that of its Lie algebra. Using an analogue of the trace map, most of the homology classes can be explained in terms of the classical cohomology of a maximal nilpotent Lie algebra, described via the root system of the semisimple Lie algebra. This could be interpreted that the singularities of the commuting scheme of a maximal nilpotent subalgebra are largely determined by root system data. If time permits, I will also discuss a possible nilpotent analogue of the Macdonald identity, together with an interpretation in terms of representation homology.
Posted October 19, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Laura Kurtz, Louisiana State University
Stochastic Homogenization
In this talk, we develop tools of stochastic homogenization of elliptic operators. We focus mainly on the periodic case and discuss the implications of the stochastic case.
Event contact: Moises Gomez-Solis
Posted October 6, 2025
Last modified October 8, 2025
Paul Kirk, Indiana University
The SU(2) character variety "Functor" from the bordism category of 2+1 manifolds to the Weinstein symplectic "category"
Around 1990, Atiyah-Floer made a "conjecture" advocating for the study of 3-manifolds by using the symplectic properties of the SU(2) character varieties of 2 and 3-manifolds. This conjecture and surrounding philosophy has had a profound influence on the development of low dimensional topology ever since (with its most powerful consequences the construction of Heegard-Floer theory and the growth of symplectic topology). I'll explain what all these words mean in down to earth terms, and why there are "scare quotes" everywhere, and discuss history and related areas of mathematics. Tip: To help you get something out of the talk, spend a few minutes looking at: (a) the definition of the fundamental group of a space, and the Seifert-Van Kampen theorem, (b) the definition of the quaternions, and in particular the unit quaternions=SU(2), and (c) the definition of a symplectic manifold and a Lagrangian submanifold.
Posted August 27, 2025
Last modified October 22, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Remi Mandal, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted September 1, 2025
Last modified October 9, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Haulmark, UT Rio Grande Valley
Cubes from Divisions
Actions on CAT(0) cube complexes have played an important role in advances in low-dimensional topology. Most notably, they are central to Wise's Quasiconvex Hierarchy Theorem and Agol's proof of the Virtual Haken Conjecture. In group theory, one way of obtaining an action on a cube complex is via the Sageev construction. Given a group G and a collection of codimension-1 subgroups of G, Sageev's construction gives an isometric action on a CAT(0) cube complex. In recent work with Jason Manning, we give an alternate route to the Sageev construction, which is potentially applicable to new situations. Much of this talk will be spent on background. We will introduce the notion of a wall space, as well as the cube complex dual to a wallspace. We will then construct an action on a CAT(0) cube complex given a group action on a sufficiently nice topological space and a system of divisions of that space.
Posted October 6, 2025
Last modified October 13, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Paul Kirk, Indiana University
On the SU(2) character variety of a closed oriented genus 2 surface
A celebrated theorem of Narasimhan-Ramanan asserts that the singular variety $X(F_2)=Hom(\pi_1(F_2),SU(2))/Conjugation$ is homeomorphic to $CP^3$. The proof passes through the (mysterious) Narasimhan-Seshadri correspondence. I'll outline an elementary differential topology proof that $X(F_2)$ is a manifold, homeomorphic to CP^3, and discuss how 3-manifolds with genus 2 boundary determine embedded lagrangians in $X(F_2)$. If time permits, I'll end the talk with a discussion of context, particularly with a program known as the Atiyah-Floer conjecture.
Posted September 5, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Naira Hovakimyan, University of Illinois Urbana-Champaign
Fellow of AIAA, ASME, IEEE, and IFAC
Safe Learning in Autonomous Systems
Learning-based control paradigms have seen many success stories with autonomous systems and robots in recent years. However, as these robots prepare to enter the real world, operating safely in the presence of imperfect model knowledge and external disturbances is going to be vital to ensure mission success. We introduce a class of distributionally robust adaptive control architectures that ensure robustness to distribution shifts and enable the development of certificates for validation and verification of learning-enabled systems. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications.
Posted October 22, 2025
LSU AWM Student Chapter LSU AWM Student Chapter Website
11:30 am – 12:20 pm https://lsu.zoom.us/j/7469727061?pwd=Q1E1b0lUL1Z3WnJxY1lTNVRtVVNmUT09
Naira Hovakimyan, University of Illinois Urbana-Champaign
Fellow of AIAA, ASME, IEEE, and IFAC
Q&A session with Dr. Naira Hovakimyan
This is an online event (over Zoom) following her talk on Safe Learning in Autonomous Systems at the Control and Optimization seminar. This is an opportunity to engage with Professor Naira Hovakimyan in an informal setting and ask questions about her research, career path, and experiences in Mathematics and Engineering.
Event contact: jgarc86@lsu.edu
Posted October 17, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 click here to attend on Zoom
Christine Cho, Louisiana State University
The symmetric strong circuit elimination property
A set $\mathcal{C}$ of incomparable non-empty subsets of a finite set $E$ is the set of circuits of a matroid on $E$ when $\mathcal{C}$ satisfies either the weak circuit elimination axiom or the strong circuit elimination axiom. The strong circuit elimination axiom is inherently asymmetric. In this talk, we will present the symmetric strong circuit elimination property (SSCE) and characterize the class of connected matroids that possess this property. We will also explore the notion of skew circuits in a matroid, both in relation to the class of matroids satisfying SSCE and beyond. This talk is based on joint work with James Oxley and Suijie Wang.
Posted September 9, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kalani Thalagoda, Tulane University
A summation formula for Hurwitz class numbers
The Hurwitz class numbers, $H(n)$, count ${\rm SL}(2,\mathbb{Z})$-classes of binary quadratic forms inversely weighted by stabilizer size. They are famously connected to the sum of three squares problem and to class numbers of imaginary quadratic fields. The work of Zagier in 1975 showed that their generating functions are related to a weight $3/2$ Harmonic Maass form. In this talk, I will discuss a summation formula for mock modular forms of moderate growth, with an emphasis on its application to Hurwitz class numbers. This is joint work with Olivia Beckwith, Nicholas Diamantis, Rajat Gupta, and Larry Rolen.
Posted October 27, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Monday, October 27, 2025 Lockett 136
Sanjeet Sahoo, LSU
Introduction to Invariant Measures and Ergodicity for Markov Processes
In this talk, we will introduce the concept of transition probability measures and establish criteria for the existence and uniqueness of invariant measures.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted September 1, 2025
Last modified October 29, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Chen Zhang, Simons Center for Geometry and Physics
Plane Floer homology and the odd Khovanov homology of 2-knots
In this talk, I will discuss joint work with Spyropoulous and Vidyarthi in which we prove a conjecture of Migdail and Wehrli regarding the maps which odd Khovanov homology associates to knotted spheres. Our main tool is the spectral sequence from reduced OKH to Plane Floer homology.
Posted October 7, 2025
Last modified October 9, 2025
Control and Optimization Seminar Questions or comments?
9:30 am – 10:20 am Note: First of 2 Seminars for 10/31. Zoom (click here to join)
Alexandre Mauroy, Université de Namur
Dual Koopman Operator Formulation in Reproducing Kernel Hilbert Spaces for State Estimation
The Koopman operator acts on observable functions defined over the state space of a dynamical system, thereby providing a linear global description of the system dynamics. A pointwise description of the system is recovered through a weak formulation, i.e. via the pointwise evaluation of observables at specific states. In this context, the use of reproducing kernel Hilbert spaces (RKHS) is of interest since the above evaluation can be represented as the duality pairing between the observables and bounded evaluation functionals. This representation emphasizes the relevance of a dual formulation for the Koopman operator, where a dual Koopman system governs the evolution of linear evaluation functionals. In this talk, we will leverage the dual formulation to build a Luenberger observer that estimates the (infinite-dimensional) state of the Koopman dual system, and equivalently the (finite-dimensional) state of the nonlinear dynamics. The method will be complemented with theoretical convergence results that support numerical Koopman operator-based estimation techniques known from the literature. Finally, we will extend the framework to a probabilistic approach by solving the problem of moments in the RKHS setting.
Posted October 8, 2025
Last modified October 28, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Note: Second of 2 Seminars for 10/31. Zoom (click here to join)
Umesh Vaidya, Clemson University
Koopman Meets Hamilton and Jacobi: Data-Driven Control Beyond Linearity
In this talk, we present recent advances in operator-theoretic methods for controlling nonlinear dynamical systems. We begin by establishing a novel connection between the spectral properties of the Koopman operator and solutions of the Hamilton–Jacobi (HJ) equation. Since the HJ equation lies at the core of optimal control, robust control, dissipativity theory, input–output analysis, and reachability, this connection provides a new pathway for leveraging Koopman spectral representations to address control problems in a data-driven setting. In particular, we show how Koopman coordinates can shift the classical curse of dimensionality associated with solving the HJ equation into a curse of complexity that is more manageable through modern computational tools. In the second part of the talk, we discuss safe control synthesis using the Perron–Frobenius operator. A key contribution is the analytical construction of a navigation density function that enables safe motion planning in both static and dynamic environments. We further present a convex optimization formulation of safety-constrained optimal control in the dual (density) space, allowing safety constraints to be incorporated systematically. Finally, we demonstrate the application of this unified operator-theoretic framework to the control of autonomous ground vehicles operating in off-road environments.
Posted October 27, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Matthew Mizell, LSU
Unavoidable minors of matroids with minimum cocircuit size four
When a graph $G$ is a 2-connected and loopless, the set of edges that meet a fixed vertex of $G$ is a bond of $G$ and a cocircuit of its cycle matroid $M(G)$. Because of this, it is common in matroid theory to take minimum cocircuit size as a matroid analog of minimum vertex degree in a graph. Halin and Jung proved in 1963 that every simple graph with minimum degree at least four has $K_5$ or $K_{2,2,2}$ as a minor. In this talk, we will provide a characterization of matroids with minimum cocircuit size four in terms of their unavoidable minors. This talk is based on joint work with James Oxley.
Posted October 21, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Michael Lacey, Georgia Institute of Technology
Prime Wiener Wintner Theorem
The classical Wiener Wintner Theorem has an extension to prime averages. Namely, for all measure preserving system $(X,m,T)$, and bounded function $f$ on $X$, there is a set of full measure $X_f\subset X$ so that for all $x\in X_f$, the averages below $$ \frac 1N \sum_{n=1}^N \phi(n) \Lambda (n) f(T^n x ) $$ converge for all continuous $2\pi$ periodic $\phi $. Above, $\Lambda$ is the von Mangoldt function. The proof uses the structure theory of measure preserving systems, the Prime Ergodic Theorem, and higher order Fourier properties of the Heath-Brown approximate to the von Mangoldt function. Joint work with J. Fordal, A. Fragkos, Ben Krause, Hamed Mousavi, and Yuchen Sun.
Posted October 22, 2025
Last modified October 23, 2025
Southern Regional Harmonic Analysis Conference
The Southern Regional Harmonic Analysis Conference will focus on current research in harmonic analysis and its applications, featuring plenary talks by Michael Lacey and Irina Holmes. For more details, please refer to conference webpage: https://www.math.lsu.edu/~ha2025/
Event contact: Rui Han, Gestur Olafsson, Naga Manasa Vempati, Fan Yang
Posted October 26, 2025
Last modified November 1, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Che-Wei Hsu, National Taiwan University
Hypergeometric Evaluations of L-values and Harmonic Maass Forms
In their earlier work, Bruinier, Ono, and Rhoades asked for an explicit construction of good harmonic Maass forms associated with CM newforms. Building on Ramanujan's theories of elliptic functions to alternative bases, we express $L$-values of certain weakly holomorphic cusp forms in terms of hypergeometric functions. As an application, we construct harmonic Maass forms with explicitly computable Fourier coefficients that are good for specific Hecke eigenforms including certain CM cusp forms.
In this talk, I will briefly review the basic notions of harmonic Maass forms and then present the ongoing joint work with Jia-Wei Guo, Fang-Ting Tu, and Yifan Yang.
Posted October 29, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm Lockett 136
Christopher Bunting, LSU
Ergodicity of solutions to the stochastic Navier-Stokes equations
The stochastic Navier-Stokes equations has been extensively studied over the past few decades. In this talk, we consider the 2D stochastic Navier-Stokes equations perturbed by an additive noise. We begin by establishing results regarding solutions and provide essential estimates. Using these results, we prove the existence and uniqueness of invariant measure for the solutions of the equations.
Event contact: Laura Kurtz