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 16, 2023

Last modified March 27, 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 March 29, 2023

Informal Geometry and Topology Seminar Questions or comments?

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

Posted January 18, 2023

Last modified March 28, 2023

Geometry and Topology Seminar Seminar website

3:30 pm Lockett 233
Allison Miller, Swarthmore

Generalizing sliceness

A knot in the 3-sphere is said to be smoothly slice if it bounds a smoothly embedded disc in the 4-ball. Sliceness questions are closely related to interesting phenomena in 4-manifold topology: for example, the existence of a non smoothly slice knot that bounds a flatly embedded disc can be used to give a relatively quick proof of the existence of nonstandard smooth structures on 4-dimensional euclidean space. There are (at least!) two reasonable generalizations of sliceness to arbitrary 4-manifolds: in each of these directions, we will highlight open questions and give some results from joint work with Kjuchokova-Ray-Sakallı and Marengon-Ray-Stipsicz.

Posted February 23, 2023

Last modified March 29, 2023

Markus Hunziker, Baylor University

Associated varieties and unitarizability of highest weight Harish-Chandra modules

In the first part of this talk, we will explain how to determine the associated variety of any highest weight Harish-Chandra module directly from its highest weight by computing the width of a poset. In the second part, we will see how this leads to a simple new characterization of unitarizability of some highest weight Harish-Chandra modules. This is a joint work with Zhangqiang Bai.

Posted March 26, 2023

Last modified March 31, 2023

Probability Seminar Questions or comments?

Zoom
Samy Tindel, Purdue University

Hyperbolic Anderson model in the Skorohod and rough settings

In this talk I will start by giving a brief overview of some standard results concerning the stochastic heat equation, for which existence and uniqueness results are well established for a large class of Gaussian noises. Then I will describe some recent advances aiming at a proper definition of noisy wave equations, when specialized to a bilinear setting (called hyperbolic Anderson model). First I will focus on the so-called Skorohod setting, where an explicit chaos decomposition of the solution is available. A good control of the chaos expansion is then achieved thanks to an exponentiation trick. Next I will turn to a pathwise approach, which is based on a novel Strichartz type estimate for the wave operator. If possible I will show the main steps of this analytic estimate.

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 March 29, 2023

Informal Geometry and Topology Seminar Questions or comments?

1:30 pm Lockett 233
Jake Murphy, LSU

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