Posted January 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Shea Vela-Vick, Louisiana State University

Characteristic Classes

Posted February 20, 2024

Faculty Meeting Questions or comments?

1:30 pm – 2:00 pm ZoomMeeting of the Professorial Faculty

Posted January 15, 2024

Last modified February 18, 2024

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Jake Murphy, LSU

Subgroups of Coxeter groups and Stallings folds

Stallings introduced a technique called a fold to study subgroups of free groups. These folds allow us to associate labeled graphs to subgroups of free groups, which in turn provide solutions to algorithmic questions about these subgroups, and Dani and Levcovitz generalized these techniques to the setting of right-angled Coxeter groups. In this talk, we will generalize these techniques to subgroups of general Coxeter groups by creating a labeled cell complex for a given subgroup. We will show that these complexes characterize the index of a subgroup and whether a subgroup is normal. Finally, we will construct a complex corresponding to the intersection of two subgroups and use this to determine whether subgroups of right-angled Coxeter groups are malnormal.

Posted February 17, 2024

Combinatorics Seminar Questions or comments?

2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Yixuan Huang, Vanderbilt University

Even and odd cycles through specified vertices

Cycles through specified vertices generalize Hamilton cycles. Given a vertex subset of a graph , we define the local connectivity on $\kappa_G(X)$ by $\min_{x,y \in X} \kappa_G(x,y)$, where $\kappa_G(x,y)$ is the minimum number of vertices or edges separating $x$ and $y$, and by Menger’s theorem, equal to the maximum number of internally disjoint $xy$-paths. We prove that if a vertex subset $X$ satisfies $\kappa_G(X) \ge k \ge3$ and $|X| > k$, then there is an even cycle through any $k$ vertices of $X$. In addition, if the block containing $X$ is non-bipartite, there is an odd cycle through any $k$ vertices of $X$. Our results extend the results based on ordinary connectivity due to Bondy and Lovász. As a corollary, we prove the existence of cycles through a particular subset in the prism graph.

Posted December 28, 2023

Last modified February 20, 2024

Control and Optimization Seminar Questions or comments?

11:30 am – 12:20 pm Zoom (Click “Questions or Comments?” to request a Zoom link)
Huyên Pham
Editor-in-Chief for SIAM Journal on Control and Optimization, 2024-

A Schrödinger Bridge Approach to Generative Modeling for Time Series

We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.

Posted November 14, 2023

Algebra and Number Theory Seminar Questions or comments?

3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom
Eleanor McSpirit, University of Virginia

TBA

Posted January 18, 2024

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Amit Kumar, Louisiana State University

Characteristic Classes

Posted January 12, 2024

Last modified February 21, 2024

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Maddalena Pismataro, University of Bologna

Cohomology rings of abelian arrangements

Abelian arrangements are generalizations of hyperplane and toric arrangements, whose complements cohomology rings have been studied since the 70’s. We introduce the complex hyperplane case, proved by Orlik and Solomon (1980), and the real case, Gelfand-Varchenko (1987). Then, we describe toric arrangements, showing results due to De Concini and Procesi (2005) and to Callegaro, D ’Adderio, Delucchi, Migliorini, and Pagaria (2020). Finally, we discuss a new technique to prove the Orlik-Solomon and De Concini-Procesi relations from the Gelfand-Varchenko ring and to provide a presentation of the cohomology ring of the complements of all abelian arrangements. This is a join work with Evienia Bazzocchi and Roberto Pagaria.