Posted March 2, 2023

Last modified March 23, 2023

Probability Seminar Questions or comments?

1:00 pm Lockett 135
Scott McKinley, Tulane University

Modeling, analysis and inference for the Generalized Langevin Equation

Fluctuating microparticles in biological fluids exhibit a wide range of anomalous behavior. From state switching (where the states cannot be directly observed) to memory effects, these particles are intrinsically Non-Markovian. In this talk, I will give a brief introduction to experimental observations that motivate using the generalized Langevin equation to model microparticle movement in mucus. In studying these paths a number of mathematical challenges arise, including determining the regularity and asymptotic behavior of these particles, and quantifying uncertainty when conducting inference.

Posted March 23, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Simon Riche, Université Clermont Auvergne

Characters of modular representations of reductive algebraic groups

One of the main questions in the representation theory of reductive algebraic groups is the computation of characters of simple modules. A conjectural solution to this problem was proposed by G. Lusztig in 1980, and later shown to be correct assuming the base field has large characteristic. However in 2013 G. Williamson found (counter)examples showing that this answer is not correct without this assumption. In this talk I will explain a new solution to this problem, obtained in a combination of works involving (among others) P. Achar and G. Williamson, which is less explicit but has the advantage of being valid in all characteristics.

Posted January 16, 2023

Last modified March 26, 2023

Algebra and Number Theory Seminar Questions or comments?

3:10 pm - 4:00 pm Zoom (click here)
Piper H, University of Toronto

Joint Shapes of Quartic Fields and Their Cubic Resolvents

In studying the (equi)distribution of shapes of quartic number fields, one relies heavily on Bhargava’s parametrizations which brings with it a notion of resolvent ring. Maximal rings have unique resolvent rings so it is possible to live a long and healthy life without understanding what they are. The authors have decided, however, to forsake such bliss and look into what ever are these rings and what happens if we consider their shapes along with our initial number fields. What happens is very nice! Until it isn't! We'd have more to say if our respective jobs had treated us humanely during the global pandemic, which coincidentally, is ongoing. (with Christelle Vincent)

Posted January 31, 2023

Last modified March 17, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Colton Sandvick, Louisiana State University

Singular Support of Étale Constructible Sheaves and Applications to Representation Theory

In this talk, we will discuss a generalization of singular support for constructible sheaves on manifolds where we instead consider étale constructible sheaves on algebraic varieties. Singular support in this setting was only recently defined by Beilinson in 2015. We will detail the nuances in working with étale sheaves on algebraic varieties rather than sheaves on manifolds. We will investigate a few classical applications of singular support which provides a geometric description of character sheaves in characteristic 0. We will then use Beilinson's generalization to explain some recent work of Psaromiligkos which generalizes one of these results to character sheaves on reductive groups in positive characteristic.

Posted January 10, 2023

Last modified March 13, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Jonathan Johnson, Oklahoma State University

Non-standard orders on torus bundles with one boundary

Consider a torus bundle over the circle with one boundary. Perron-Rolfsen shows that having an Alexander polynomial with real positive roots is a sufficient condition for a surface bundle with one boundary to have bi-orderable fundamental group. This is done by showing the action induced by the monodromy preserves a "standard" bi-ordering of the fundamental group of the surface. In this talk, we discuss if there are other ways to bi-order the fundamental group of a torus bundle with one boundary component. This work is joint with Henry Segerman. This work is partially funded by NSF grant DMS-2213213.

Posted February 23, 2023

Last modified March 24, 2023

Vishwa Dewage, Clemson University

Dense subsets of the Toeplitz algebra on the Fock space

We study the full Toeplitz algebra via convolutions of operators and the laplacian of the Berezin transform. We present a new class of operators that are dense in the Toeplitz algebra. We use this new dense class of operators to provide a new proof for the fact that the radial Toeplitz algebra is isomorphic to the space of bounded sequences that are uniformly continuous with respect to the square-root metric. This is a joint work with Mishko Mitkovski.

Posted February 9, 2023

Last modified February 24, 2023

Colloquium Questions or comments?

3:30 pm - 4:20 pm Lockett 232
Melody Chan, Brown University

Moduli spaces of graphs

My goal is to share with you a broad view on the topic of moduli spaces of graphs. A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs’’ to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.

Posted February 13, 2023

Last modified March 7, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Ningshi Yao, George Mason University

Resolving Contentions Through Real-Time Control and Scheduling for Cyber Physical Human Systems

Shared resources, such as cloud computing and communication networks, are widely used in large-scale real-time systems to increase modularity and flexibility. When multiple systems need to access a shared resource at the same time and the demands exceed the total supply, a contention occurs. A scheduling strategy is needed to determine which systems can access the resource first to resolve contentions. However, such a scheduling mechanism inevitably introduces time-varying delays and may degrade the system performance or even sabotage the stability of control systems. Considering the coupling between scheduling and control, this talk presents a novel sample-based method to co-design scheduling strategies and control laws for coupled control systems with shared resources, which aims to minimize the overall performance degradation caused by contentions. The co-design problem is formulated as a mixed integer optimization problem with a very large search space, rendering difficulty in computing the optimal solution. To solve this challenge, we describe a contention resolving model predictive control (CRMPC) method to dynamically design optimal scheduling and control in real-time. With fundamental assumptions in scheduling theory, the solution computed by CRMPC can be proved to be globally optimal. CRMPC is a theoretical framework that is general and can be applied to many applications in cyber-physical-human systems. The effectiveness of CRMPC has been verified in real-world applications, such as networked control systems, traffic intersection management systems, and human multi-robot collaboration systems. The performance of CRMPC was compared with well-known scheduling methods and demonstrated significant improvements.

Posted February 25, 2023

Last modified March 22, 2023

Association for Women in Mathematics Student Colloquium

1:30 pm - 2:30 pm Lockett Hall 277
Melody Chan, Brown University

Counting in the presence of symmetry (counting with groupoids)

Objects with symmetry are special. In many situations arising in nature, they tend to appear less frequently, in fact with frequency inverse proportional to the order of the symmetry group. I will explain some combinatorics in the presence of symmetry that can be summarized as "counting with groupoids." The student colloquium will be preceded by lunch and an informal "Ask me anything!" discussion with the speaker.

Posted February 11, 2023

Last modified March 26, 2023

Probability Seminar Questions or comments?

1:00 pm - 2:00 pm Lockett 135
Wasiur KhudaBukhsh, University of Nottingham

Large-graph approximations for interacting particles on graphs and their applications

In this talk, we will consider stochastic processes on (random) graphs. They arise naturally in epidemiology, statistical physics, computer science and engineering disciplines. In this set-up, the vertices are endowed with a local state (e.g., immunological status in case of an epidemic process, opinion about a social situation). The local state changes dynamically as the vertex interacts with its neighbours. The interaction rules and the graph structure depend on the application-specific context. We will discuss (non-equilibrium) approximation methods for those systems as the number of vertices grow large. In particular, we will discuss three different approximations in this talk: i) approximate lumpability of Markov processes based on local symmetries (local automorphisms) of the graph, ii) functional laws of large numbers in the form of ordinary and partial differential equations, and iii) functional central limit theorems in the form of Gaussian semi-martingales. We will also briefly discuss how those approximations could be used for practical purposes, such as parameter inference from real epidemic data (e.g., COVID-19 in Ohio), designing efficient simulation algorithms etc.

Posted January 31, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Jake Murphy, LSU

Posted February 23, 2023

3:30 pm - 4:30 pm TBA
Markus Hunziker, Baylor University

TBA

Posted January 18, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Allison Miller, Swarthmore

Posted March 26, 2023

Probability Seminar Questions or comments?

Samy Tindel, Purdue University

TBA

Posted February 1, 2023

Last modified March 20, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett Hall 232
Kirill Cherednichenko, University of Bath

Operator-norm homogenisation for Maxwell equations on periodic singular structures

I will discuss a new approach to obtaining uniform operator asymptotic estimates in periodic homogenisation. Based on a novel uniform Poincaré-type inequality, it bears similarities to the techniques I developed with Cooper (ARMA, 2016) and Velcic (JLMS, 2022). In the context of the Maxwell system, the analytic framework I will present leads to a new representation for the asymptotics obtained by Birman and Suslina in 2007 for the full system and by Suslina in 2004 for the electric field in the presence of currents. As part of the new asymptotic construction, I will link the leading-order approximation to a family of "homogenised" problems, which was not possible using the earlier method. The analysis presented applies to a class of inhomogeneous structures modelled by arbitrary periodic Borel measures. However, the results are new even for the particular case of the Lebesgue measure. This is joint work with Serena D'Onofrio.

Posted January 31, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Gurleen Nanda, Louisiana State University

Posted January 10, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Giovanni Paolini, Caltech

Posted January 18, 2023

Last modified March 2, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maruthi Akella, University of Texas
Fellow of AIAA, IEEE, and AAS

Sub-Modularity Measures for Learning and Robust Perception in Aerospace Autonomy

Onboard learning and robust perception can be generally viewed to characterize autonomy as overarching system-level properties. The complex interplay between autonomy and onboard decision support systems introduces new vulnerabilities that are extremely hard to predict with most existing guidance and control tools. In this seminar, we review some recent advances in learning-oriented and information-aware path- planning, and sub-modularity metrics for non-myopic sensor scheduling for “plug-and- play” systems. The concept of “learning-oriented” path-planning is realized through certain new classes of exploration inducing distance metrics. These technical foundations will be highlighted through aerospace applications with active learning inside dynamic and uncertain environments.

Posted February 11, 2023

Probability Seminar Questions or comments?

1:00 pm - 2:00 pm Zoom
Adina Oprisan, New Mexico State University

TBA

Posted January 11, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Melissa Sherman-Bennett, MIT

TBA

Posted January 31, 2023

Informal Geometry and Topology Seminar Questions or comments?

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

Posted January 10, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Chindu Mohanakumar, Duke University

Posted December 12, 2022

Last modified March 6, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Maria Elena Valcher, University of Padova
Fellow of IEEE and of IFAC

TBA

Posted January 21, 2023

Last modified March 8, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Svetlana Makarova, University of Pennsylvania

Quiver moduli and effective global generation

Moduli problems are ubiquitous and related to all areas of mathematics in one way or another. In this talk, I will focus on the algebro-geometric picture: namely, I would like to view the set of objects of classification as a scheme, called a moduli scheme. I will provide a framework that allows to recover the algebraic structure on this set, and then I will talk about modern methods of studying moduli problems. The modern theory "Beyond GIT", introduced by Alper and being developed by Alper, Halpern-Leistner, Heinloth and others, provides a "coordinate-free" way of thinking about classification problems. Among giving a uniform philosophy, this allows to treat problems that can't necessarily be described as global quotients. Our result about moduli of quiver representations is a particularly nice example where this modern theory can be applied. After a reminder on quiver representations, I will explain how we refine a classical result of King that moduli spaces of semistable representations of acyclic quivers are projective by proving it over an arbitrary noetherian base. Our methods allow us to obtain new results about the geometry of these moduli: I will define a determinantal line bundle which descends to a semiample line bundle on the moduli space and provide effective bounds for its global generation. For an acyclic quiver, we can observe that this line bundle is ample and thus the adequate moduli space is projective over an arbitrary noetherian base. This talk is based on a preprint with Belmans, Damiolini, Franzen, Hoskins, Tajakka (https://arxiv.org/abs/2210.00033).

Posted February 28, 2023

Last modified March 7, 2023

Applied Analysis Seminar Questions or comments?

3:30 pm - 4:30 pm Zoom
Hung Tran, University of Wisconsin Madison

TBA

Posted January 12, 2023

Computational Mathematics Seminar

3:30 pm - 4:20 pm LDMC: room 1034
Matthias Maier, Department of Mathematics Texas A&M University

TBA

Posted January 31, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Megan Farrell, Louisiana State University

Posted January 10, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Ying Hu, University of Nebraska Omaha

Posted January 17, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Weiwei Hu, University of Georgia

TBA

Posted January 9, 2023

Mathematical Physics and Representation Theory Seminar

2:30 pm - 3:20 pm Lockett 233
Anne Dranowski, University of Southern California

TBA

Posted January 31, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Matthew McCoy, Louisiana State University

Posted January 11, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Ben Knudsen, Northeastern University

Posted January 26, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Wim Michiels, KU Leuven

TBA

Posted February 13, 2023

Last modified February 14, 2023

Control and Optimization Seminar Questions or comments?

10:30 am - 11:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Matthew Hale, University of Florida
AFOSR Young Investigator, ONR Young Investigator, and NSF CAREER Program Awardee

TBA

Posted December 9, 2022

Applied Analysis Seminar Questions or comments?

3:30 pm Lockett Hall 233 and Zoom
Nicolas Meunier, LaMME, Universite Evry Val D'Essonne

TBA