Calendar
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 January 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett
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 23, 2025
Last modified January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Annette Karrer, The Ohio State University
TBA
Posted January 12, 2025
Last modified January 16, 2025
Zi Li Lim, UCLA
TBA
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.