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This Week in Mathematics

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Next Week [Dec 03, 2023 - Dec 09, 2023]
Entries for this week: 5
Tuesday December 05, 2023

Topology/Geometry Seminar [url]
Smooth actions on manifold by higher rank lattices
    - Homin Lee, Northwestern
Time: 3:05 PM Room: LOV 231
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Abstract/Desc: We will discuss about smooth actions on manifolds by higher rank groups, such as lattices in SL(n,R) with n ≥ 3 or Z^k with k ≥ 2. The higher rank property of the acting group suggests that the actions are rigid, which means that the action should have an algebraic origin, such as the Zimmer program and the Katok-Spatzier conjecture. One of the main topics is about how we can give an algebraic structure on the acting space which is a smooth manifold. We survey some of recent breakthroughs and then focus mainly on actions of higher rank lattices. In particular, we focus on actions on manifold with “positive entropy” by lattices in SL(n,R), n ≥ 3. When the manifold has dimension n, then we will see that the lattice is commensurable to SL(n,Z) from certain "algebraic structure" on M coming from the dynamics. Part of the talk is ongoing work with Aaron Brown.

Wednesday December 06, 2023

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Applied and Computational Math Seminar -- Stochastic Computing and Optimization
Stochastic Computing and Optimization
    - ACM/Fin Math students,
Time: 3:05PM Room: LOV 0231
Abstract/Desc: Students from ACM and Financial Math will present their research progress. Some invited speakers may also present their research.

Biomathematics Seminar
    - Mike Cortez, FSU
Time: 3:05 Room: LOV232
Abstract/Desc: TBA

Thursday December 07, 2023

Financial Mathematics Seminar [url]
Set Values of Mean Field Games
    - Melih Iseri , University of Michigan, Ann Arbor
Time: 3:05 Room: ZOOM
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Abstract/Desc: In this talk we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the mean field game. When the mean field equilibrium is unique, typically under certain monotonicity conditions, our set value reduces to the singleton of the standard value function which solves the master equation. The set value is by nature unique, and we shall establish two crucial properties: (i) the dynamic programming principle, which is essential for a future PDE approach; and (ii) the convergence of the set values of the corresponding N -player games. To our best knowledge, this is the first work in the literature which studies the dynamic value of mean field games without requiring the uniqueness of mean field equilibria. We emphasize that the set value is very sensitive to the choice of the admissible controls. In particular, for the convergence one has to restrict to the same type of equilibria for the N-player game and for the mean field game. We shall illustrate this point by investigating three cases, two in finite state space models and the other in a diffusion model.

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