Published on Department of Mathematics Calendar (https://calendar.math.yale.edu)

Week of November 12, 2023

November 13, 2023
Group Actions, Geometry and Dynamics [3]	Stationary probability measures on projective spaces	Cagri Sert - University of Zurich	4:00pm - KT801

November 15, 2023
Colloquium [4]	Geometry and Dynamics of Anosov groups	Richard Canary - University of Michigan - Ann Arbor	4:00pm - KT 219

November 16, 2023
Group Actions, Geometry and Dynamics [3]	Transverse groups and relatively Anosov groups	Richard Canary - University of Michigan	4:00pm - KT205
Analysis [5]	Generalized Bessel Functions in High Dimension	Colin McSwiggen - NYU Courant	4:00pm - KT 219
	Learning seminar on D-modules	Trung Vu - Yale	4:00pm - KT 801

November 17, 2023
Friday Morning Seminar [6]	Friday Morning Seminar		10:00am - KT 801
Geometric Analysis and Application [7]	Positive scalar curvature metric and aspherical summands	Shuli Chen - Stanford University	2:00pm - KT 906

Abstracts

Week of November 12, 2023

November 13, 2023
Group Actions, Geometry and Dynamics [3]	Stationary probability measures on projective spaces	4:00pm - KT801	We give a description of stationary probability measures on projective spaces for an iid random walk on GLd(R) without any algebraic assumptions. This is done in two parts. In a first part, we study the case (non-critical or block-dominated case) where the random walk has distinct deterministic exponents in the sense of Furstenberg-Kifer-Hennion. In a second part (critical case), we show that if the random walk has only one deterministic exponent, then any stationary probability measure on the projective space lives on a subspace on which the ambient group of the random walk acts completely reducibly. This connects the critical setting with the work of Guivarc’h-Raugi and Benoist-Quint. Combination of all these works allow to get a description of stationary probability measures. Joint works with Richard Aoun.

November 15, 2023
Colloquium [4]	Geometry and Dynamics of Anosov groups	4:00pm - KT 219	Francois Labourie introduced the theory of Anosov subgroups of semi-simple Lie groups in his seminal work on Hitchin representations. Anosov groups are now widely recognized as the higher rank generalization of convex cocompact subgroups of rank one Lie groups. (For our purposes, all higher rank Lie groups will be SL(d,R) and rank one Lie groups will all be PSL(2,R), PSL(2,C) or SO(d,1).) We will review classical results on convex cocompact subgroups of rank one Lie groups and discuss how they generalize into the setting of Anosov groups.

November 16, 2023
Group Actions, Geometry and Dynamics [3]	Transverse groups and relatively Anosov groups	4:00pm - KT205	Transverse subgroups of semi-simple Lie groups include all discrete subgroups of rank one Lie groups and Anosov and relatively Anosov subgroups of higher rank Lie groups. Every transverse group comes equipped with a family of “geodesic flows’’ associated to linear functionals on the Cartan subspace. The assumption of transversality allows for the construction of well-behaved Patterson-Sullivan measures on the limit set and associated Bowen-Margulis-Sullivan measures on the flows. We discuss a Hopf-Tsuji-Sullivan dichotomy in this context. Finally, we show that relatively Anosov groups live on the divergent side of this dichotomy (Joint work with Tengren Zhang and Andy Zimmer)
Analysis [5]	Generalized Bessel Functions in High Dimension	4:00pm - KT 219	Many quantities of interest throughout mathematics are basically Bessel functions of a vector argument. As a result, natural asymptotic questions in various fields can be reduced to understanding the behavior of multivariable Bessel functions as the dimension of the domain grows large. In this talk, I’ll introduce the theory of generalized Bessel functions and describe how these functions form a useful link between subjects as diverse as random matrix theory, harmonic analysis and integrable systems. Then I’ll present a new result that characterizes the high-dimensional asymptotics of generalized Bessel functions by studying the hydrodynamics of associated stochastic processes. Joint work with Jiaoyang Huang (https://arxiv.org/abs/2305.04131 [10]).
	Learning seminar on D-modules	4:00pm - KT 801	This is the 9th lecture in the series.

November 17, 2023
Friday Morning Seminar [6]	Friday Morning Seminar	10:00am - KT 801	A relaxed-pace seminar on impromptu subjects related to the interests of the audience. Everyone is welcome. The subjects are geometry, probability, combinatorics, dynamics, and more!
Geometric Analysis and Application [7]	Positive scalar curvature metric and aspherical summands	2:00pm - KT 906	Abstract: It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. A manifold is called aspherical if it has contractible universal cover. By works of Chodosh—Li, Gromov, and Chodosh—Li—Liokumovich, for n = 4, 5, the connected sum of a closed aspherical n-manifold with an arbitrary closed manifold does not admit a metric with positive scalar curvature. We prove that for n = 3,4,5, the connected sum of a closed aspherical n-manifold with an arbitrary non-compact manifold does not admit a complete metric with nonnegative scalar curvature. In particular, a special case of our result answers a question of Gromov. This is joint work with Jianchun Chu and Jintian Zhu.

Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W45 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2023-W47 [3] https://calendar.math.yale.edu/seminars/group-actions-geometry-and-dynamics [4] https://calendar.math.yale.edu/seminars/colloquium [5] https://calendar.math.yale.edu/seminars/analysis [6] https://calendar.math.yale.edu/seminars/friday-morning-seminar [7] https://calendar.math.yale.edu/seminars/geometric-analysis-and-application [8] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W45 [9] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2023-W47 [10] https://arxiv.org/abs/2305.04131