Posted January 22, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Dante Kalise, Imperial College
Feedback Control Synthesis for Interacting Particle Systems across Scales
This talk focuses on the computational synthesis of optimal feedback controllers for interacting particle systems operating at different scales. In the first part, we discuss the construction of control laws for large-scale microscopic dynamics by supervised learning methods, tackling the curse of dimensionality inherent in such systems. Moving forward, we integrate the microscopic feedback law into a Boltzmann-type equation, bridging controls at microscopic and mesoscopic scales, allowing for near-optimal control of high-dimensional densities. Finally, in the framework of mean field optimal control, we discuss the stabilization of nonlinear Fokker-Planck equations towards unstable steady states via model predictive control.
Posted March 5, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm 233 Lockett
Pablo Boixeda Alvarez, Yale University
Microlocal sheaves and affine Springer fibers
The resolutions of Slodowy slices $\tilde{\mathcal{S}}_e$ are symplectic varieties that contain the Springer fiber $(G/B)_e$ as a Lagrangian subvariety. In joint work with R. Bezrukavnikov, M. McBreen, and Z. Yun, we construct analogues of these spaces for homogeneous affine Springer fibers. We further understand the categories of microlocal sheaves in these symplectic spaces supported on the affine Springer fiber as some categories of coherent sheaves. In this talk, I will mostly focus on the case of the homogeneous element $ts$ for $s$, a regular semisimple element, and will discuss some relations of these categories with the small quantum group providing a categorification of joint work with R.Bezrukavnikov, P. Shan and E. Vasserot. If I have time, I will then mention some recent application of this result to the Breuil-Mezard conjecture by T. Feng and B. Le Hung.
Posted January 18, 2024
Last modified March 18, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Jake Murphy, LSU
Incoherent Coxeter groups
A group is coherent if every finitely generated subgroup is also finitely presented. In this talk, we will cover results of Jankiewicz and Wise showing that many Coxeter groups are incoherent using Bestvina-Brady Morse theory.
Posted November 29, 2023
Geometry and Topology Seminar Seminar website
3:30 pm – 4:30 pm Lockett 233
Katherine Raoux, University of Arkansas
TBA
Posted January 24, 2024
Last modified March 13, 2024
Alan Chang, Washington University in St. Louis
Venetian blinds, digital sundials, and efficient coverings
Davies's efficient covering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formulation, known as Falconer's digital sundial theorem, which states that we can construct a set in the plane to have any desired projections, up to null sets. The argument relies on a Venetian blind construction, a classical method in geometric measure theory. In joint work with Alex McDonald and Krystal Taylor, we study a variant of Davies's efficient covering theorem in which we replace lines with curves. This has a dual formulation in terms of nonlinear projections.
Posted January 20, 2024
Last modified February 5, 2024
Colloquium Questions or comments?
3:30 pm – 4:20 pm Lockett 232
Chongying Dong, UC Santa Cruz
Monstrous moonshine and orbifold theory
This introductory talk will survey the recent development of the monstrous moonshine. Conjectured by McKay-Thompson-Conway-Norton and proved by Borcherds, the moonshine conjecture reveals a deep connection between the largest sporadic finite simple group Monster and genus zero functions. From the point of view of vertex operator algebra, moonshine is a connection among finite groups, vertex operator algebras and modular forms. This talk will explain how the moonshine phenomenon can be understood in terms of orbifold theory.
Posted February 12, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Note the Special Earlier Seminar Time For Only This Week. This is a Zoom Seminar. Zoom (click here to join)
Antoine Girard, Laboratoire des Signaux et Systèmes
CNRS Bronze Medalist, IEEE Fellow, and George S. Axelby Outstanding Paper Awardee
Switched Systems with Omega-Regular Switching Sequences: Application to Switched Observer Design
In this talk, I will present recent results on discrete-time switched linear systems. We consider systems with constrained switching signals where the constraint is given by an omega-regular language. Omega-regular languages allow us to specify fairness properties (e.g., all modes have to be activated an infinite number of times) that cannot be captured by usual switching constraints given by dwell-times or graph constraints. By combining automata theoretic techniques and Lyapunov theory, we provide necessary and sufficient conditions for the stability of such switched systems. In the second part of the talk, I will present an application of our framework to observer design of switched systems that are unobservable for arbitrary switching. We establish a systematic and "almost universal" procedure to design observers for discrete-time switched linear systems. This is joint work with Georges Aazan, Luca Greco and Paolo Mason.
Posted February 17, 2024
Last modified March 18, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Samuel Punshon-Smith, Tulane University
Annealed mixing and spectral gap for advection by stochastic velocity fields
We consider the long-time behavior of a passive scalar advected by an incompressible velocity field. In the dynamical systems literature, if the velocity field is autonomous or time periodic, long-time behavior follows by studying the spectral properties of the transfer operator associated with the finite time flow map. When the flow is uniformly hyperbolic, it is well known that it is possible to construct certain anisotropic Sobolev spaces where the transfer operator becomes quasi-compact with a spectral gap, yielding exponential decay in these spaces. In the non-autonomous and non-uniformly hyperbolic case this approach breaks down. In this talk, I will discuss how in the stochastic velocity setting one can recover analogous results under expectation using pseudo differential operators to obtain exponential decay of solutions to the transport equation from $H^{-\delta}$ to $H^{-\delta}$ -- a property we call annealed mixing. As a result, we show that the Markov process obtained by considering the advection diffusion equation with a source term has an $H^{-\delta}$ Wasserstein spectral gap, uniform in diffusivity, and that the stationary measure has a unique limit in the zero diffusivity limit. This is a joint work with Jacob Bedrossian and Patrick Flynn.