Calendar

Posted February 11, 2023
Last modified March 18, 2023

Probability Seminar Questions or comments?

Pratima Hebbar, Grinnell College
Branching Diffusion in Periodic Media

We describe the behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the k-th moment dominates the k-th power of the first moment for some k), while, at distances that grow sub-linearly in time, we show that all the moments converge. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.

Posted February 20, 2023
Last modified March 3, 2023

Applied Analysis Seminar Questions or comments?

Max Engelstein, University of Minnesota
On global graphical solutions to free boundary problems

The Bernstein problem for minimal surfaces asks whether a globally defined minimal hypersurface given by the graph of a function in dimension $n$ must be a hyperplane. This was resolved by the combined work of De Giorgi, Simons and then De Giorgi-Bombieri-Giusti; showing that the answer is yes when $n \leq 8$ and no when $n\geq 9$. In this talk we will discuss recent progress towards this question for one-phase free boundary problems of Bernoulli type. This is joint with Xavier Fernandez-Real (EPFL) and Hui Yu (NUS).

Posted January 31, 2023
Last modified March 17, 2023

Informal Geometry and Topology Seminar Questions or comments?

Colton Sandvick, Louisiana State University
Singular Support of Constructible Sheaves on Manifolds

Given a sheaf F on a real manifold X, one can assign closed, conic, Lagrangian subset of the cotangent bundle T*X, called the singular support. Singular support is a powerful invariant of sheaves and behaves well with regard to many common sheaf operations. In this talk, we will discuss singular support in the context of constructible sheaves, describe many of its fundamental properties, and give some examples. As an application, we will discuss some classes of sheaves which can be described by their singular support. We will not assume any prior knowledge of sheaf theory; although, some familiarness with differential geometry and singular (or de Rham) cohomology will be helpful.

Posted January 10, 2023
Last modified March 14, 2023

Geometry and Topology Seminar Seminar website

Grigori Avramidi, Max Planck Institute for Mathematics
Division, group rings, and negative curvature

In 1997 Delzant observed that fundamental groups of hyperbolic manifolds with large injectivity radius have nicely behaved group rings. In particular, these rings have no zero divisors and only the trivial units. In this talk I will discuss an extension of this observation showing that such rings have a division algorithm (generalizing the division algorithm for group rings of free groups discovered by Cohn) and ``freedom theorems’’ saying ideals generated by two elements are free (which can be viewed as generalizations from subgroups to ideals of some freedom theorems of Delzant and Gromov). This has geometric consequences to the homotopy classification of 2-complexes with surface fundamental groups and to complexity of cell structures on hyperbolic manifolds.

Posted February 23, 2023

Harmonic Analysis Seminar

Iswarya Sitiraju, Louisiana State University
TBA

Posted February 14, 2023

Control and Optimization Seminar Questions or comments?

Frank Allgower, University of Stuttgart IFAC Fellow
Data-driven Model Predictive Control: Concepts, Algorithms and Properties

While recent years have shown rapid progress of learning-based and data-driven methods to effectively utilize data for control tasks, providing rigorous theoretical guarantees for such methods is challenging and an active field of research. This talk will be about a recently developed framework for model predictive control (MPC) of unknown systems based only on input-output data which admits exactly such guarantees. The proposed approach relies on the Fundamental Lemma of Willems et al. which parametrizes trajectories of unknown linear systems using data. First, we cover MPC schemes for linear systems with a focus on theoretical guarantees for the closed loop, which can be derived even if the data are noisy. Building on these results, we then move towards the general, nonlinear case. Specifically, we present a data-driven MPC approach which updates the data used for prediction online at every time step and, thereby, stabilizes unknown nonlinear systems using only input-output data. In addition to introducing the framework and the theoretical results, we also report on successful applications of the proposed framework in simulation and real-world experiments.

Posted March 2, 2023

Probability Seminar Questions or comments?

Scott McKinley, Tulane University
TBA