# Events for 09/23/2022 from all calendars

## Student/Postdoc Working Geometry Seminar

**Time: ** 1:30PM - 2:30PM

**Location: ** BLOC 628

**Speaker: **JM Landsberg, TAMU

**Title: ***Castelnuovo's lemma and Steiner bundles*

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** Bloc 306

**Speaker: **Alain Bensoussan, University of Texas at Dallas

**Title: ***Control On Hilbert Spaces and Mean Field Control*

**Abstract: **In this work, we describe an alternative approach to the general theory of Mean Field Control as presented in the book of P. Cardaliaguet, F. Delarue, J-M Lasry, P-L Lions: The Master Equation and the Convergence Problem in Mean Field Games, Annals of Mathematical Studies, Princeton University Press, 2019. Since it uses Control Theory and not P.D.E. techniques it applies only to Mean Field Control. The general difficulty of Mean Field Control is that the state of the dynamic system is a probability. Therefore, the natural functional space for the state is the Wasserstein metric space. P.L. Lions has suggested to use the correspondence between probability measures and random variables, so that the Wasserstein metric space is replaced with the Hilbert space of square integrable random variables. This idea is called the lifting approach. Unfortunately, this brilliant idea meets some difficulties, which prevents to use it as an alternative, except in particular cases. In using a different Hilbert space, we study a Control problem with state in a Hilbert space, which solves the original Mean Field Control problem, as a particular case, and thus provides a complete alternative to the approach of Cardaliaguet, Delarue, Lasry, Lions. Based on Joint work with P. J. GRABER, P. YAM.
Research supported by NSF grants DMS- 1905449 and 2204795.

## Geometry Seminar

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 302

**Speaker: **Runshi Geng, TAMU

**Title: ***On the geometry of geometric rank*

**Abstract: **Geometric Rank of tensors was introduced by Kopparty et al. as a useful tool to study algebraic complexity theory, extremal combinatorics and quantum information theory. In this talk I will introduce Geometric Rank and results from their paper, in particular showing the relation between geometric rank and other ranks of tensors. Then I will present recent results of geometric rank, including and the connections between geometric rank and spaces of matrices of bounded rank, and classifications of tensors with geometric rank one, two and three.