Posted January 6, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Madalena Chaves, Centre Inria d'Université Côte d'Azur
Coupling, Synchronization Dynamics, and Emergent Behavior in a Network of Biological Oscillators
Biological oscillators often involve a complex network of interactions, such as in the case of circadian rhythms or cell cycle. Mathematical modeling and especially model reduction help to understand the main mechanisms behind oscillatory behavior. In this context, we first study a two-gene oscillator using piecewise linear approximations to improve the performance and robustness of the oscillatory dynamics. Next, motivated by the synchronization of biological rhythms in a group of cells in an organ such as the liver, we then study a network of identical oscillators under diffusive coupling, interconnected according to different topologies. The piecewise linear formalism enables us to characterize the emergent dynamics of the network and show that a number of new steady states is generated in the network of oscillators. Finally, given two distinct oscillators mimicking the circadian clock and cell cycle, we analyze their interconnection to study the capacity for mutual period regulation and control between the two reduced oscillators. We are interested in characterizing the coupling parameter range for which the two systems play the roles "controller-follower".
Posted January 28, 2024
Last modified April 1, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Greg Parker, Stanford University
$\mathbb Z_2$-harmonic spinors as limiting objects in geometry and topology
$\mathbb Z_2$-harmonic spinors are singular solutions of Dirac-type equations that allow topological twisting around a submanifold of codimension 2. These objects arise as limits at the boundary of various moduli spaces in several distinct areas of low-dimensional topology, gauge/Floer theory, and enumerative geometry. The first part of this talk will introduce these objects, and discuss the various contexts in which they arise and the relationship between them. The second part of the talk will focus on the deformations of $\mathbb Z_2$-harmonic spinors when varying background parameters as a model for the novel analytic problems presented by these objects. In particular, the deformations of the singular submanifold play a role, giving the problem some characteristics similar to a free-boundary-value problem and leading to a hidden elliptic pseudo-differential operator that governs the geometry of the moduli spaces.
Posted February 21, 2024
Last modified April 12, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications
The purpose of this talk is to give an overview of recent work involving differential equations posed on spaces of probability measures and their use in analyzing mean field limits of controlled multi-agent systems, which arise in applications coming from macroeconomics, social behavior, and telecommunications. Justifying this continuum description is often nontrivial and is sensitive to the type of stochastic noise influencing the population. We will describe settings for which the convergence to mean field stochastic control problems can be resolved through the analysis of the well-posedness for a certain Hamilton-Jacobi-Bellman equation posed on Wasserstein spaces, and how this well-posedness allows for new convergence results for more general problems, for example, zero-sum stochastic differential games of mean-field type.
Posted January 18, 2024
Last modified April 19, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Megan Fairchild, Louisiana State University
The Double Branched Cover of the Three-Sphere Over a Knot.
In this talk, we will examine how the double branched cover of the three-sphere over a knot is constructed and the linking form defined on its first homology. We will discuss how to calculate first homology, defining the linking form, and calculating the linking form given a knot diagram. The main goal of the talk is to better understand this object and examine its connection to non-orientable 4-genus of knots.
Posted January 31, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Morgan Weiler, Cornell University
TBA
Posted April 19, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233
Ryan Martin, Iowa State University
Counting cycles in planar graphs
Basic Tur\'an theory asks how many edges a graph can have, given certain restrictions such as not having a large clique. A more generalized Tur\'an question asks how many copies of a fixed subgraph $H$ the graph can have, given certain restrictions. There has been a great deal of recent interest in the case where the restriction is planarity. In this talk, we will discuss some of the general results in the field, primarily the asymptotic value of ${\bf N}_{\mathcal P}(n,H)$, which denotes the maximum number of copies of $H$ in an $n$-vertex planar graph. In particular, we will focus on the case where $H$ is a cycle. It was determined that ${\bf N}_{\mathcal P}(n,C_{2m})=(n/m)^m+o(n^m)$ for small values of $m$ by Cox and Martin and resolved for all $m$ by Lv, Gy\H{o}ri, He, Salia, Tompkins, and Zhu. The case of $H=C_{2m+1}$ is more difficult and it is conjectured that ${\bf N}_{\mathcal P}(n,C_{2m+1})=2m(n/m)^m+o(n^m)$. We will discuss recent progress on this problem, including verification of the conjecture in the case where $m=3$ and $m=4$ and a lemma which reduces the solution of this problem for any $m$ to a so-called ``maximum likelihood'' problem. The maximum likelihood problem is, in and of itself, an interesting question in random graph theory. This is joint work with Emily Heath and Chris (Cox) Wells.
Posted January 17, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Tobias Breiten, Technical University of Berlin
On the Approximability of Koopman-Based Operator Lyapunov Equations
Computing the Lyapunov function of a system plays a crucial role in optimal feedback control, for example when the policy iteration is used. This talk will focus on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay, which justifies finite rank approximations with numerical methods. The usefulness for numerical computations will also be demonstrated with two short examples. This is joint work with Bernhard Höveler (TU Berlin).
Posted September 24, 2023
Last modified March 3, 2024
Algebra and Number Theory Seminar Questions or comments?
3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom
Ana Bălibanu, Louisiana State University
TBA
Posted February 1, 2024
Last modified February 11, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Jean-François Lafont, The Ohio State University
TBA
Posted April 16, 2024
Faculty Meeting Questions or comments?
3:00 pm – 4:00 pmMeeting 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 March 21, 2024
8:30 am – 4:40 pm 205 Prescott HallOrder, Algebra, Logic, and Real Algebraic Geometry (Day 1 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
8:30 am – 4:40 pm 205 Prescott HallOrder, Algebra, Logic, and Real Algebraic Geometry (Day 2 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
8:30 am – 12:00 pm 205 Prescott HallOrder, Algebra, Logic, and Real Algebraic Geometry (Day 3 of 3)
https://www.math.lsu.edu/OAL-RAG2024
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