Week of September 24, 2023

September 27, 2023
Applied Mathematics Two Techniques Involving High-Dimensional Data Kevin O'Neill - Yale University 3:00pm -
LOM 214
Colloquium Postdoc Intro talks Or Landesberg, Kevin O’Neill, Ka Ho Wong, and Abinand Gopal. - 4:00pm -
September 28, 2023
Graduate Learning Seminar Learning seminar on D-modules Soumik Ghosh - Yale 4:00pm -
Prospect 204, B-02
Group Actions, Geometry and Dynamics Growth indicators and conformal measures for transverse subgroups. Hee Oh - Yale University 4:00pm -
KT801
September 29, 2023
Friday Morning Seminar Friday Morning Seminar 10:00am -
809 Commons

Abstracts

Week of September 24, 2023

September 27, 2023
Applied Mathematics Two Techniques Involving High-Dimensional Data 3:00pm -
LOM 214

Data in high dimensional Euclidean space may often be described with fewer parameters than the ambient space, perhaps lying on or near a submanifold of lower intrinsic dimension. In part one of this talk, we will discuss a new method for estimating this intrinsic dimension from the data: a version of local PCA which is calibrated on quadratic embeddings which may better approximate a manifold at larger scales. The second part of the talk will focus on a technique of random embeddings to reduce ambient dimension. The topics of this talk are joint work with Anna Gilbert.
Colloquium Postdoc Intro talks 4:00pm -

Titles of the mini-talks:

Or Landesberg: (Non-)Rigidity of horocycle dynamics in geometrically infinite spaces

Kevin O’Neill: Nonlinear variants of the Whitney Extension Problem

Ka Ho Wong: Volume conjectures for quantum invariants

Abinand Gopal: Using rational functions to solve PDEs
September 28, 2023
Graduate Learning Seminar Learning seminar on D-modules 4:00pm -
Prospect 204, B-02

This is the third lecture in the seminar.
Group Actions, Geometry and Dynamics Growth indicators and conformal measures for transverse subgroups. 4:00pm -
KT801
Let $G$ be a connected semisimple real algebraic group. Let $\theta$ be a non-empty subset consisting of simple roots of $G$. The class of $\theta$-transverse subgroups of $G$ includes all discrete subgroups of rank one Lie groups, $\theta$-Anosov subgroups and their relative versions. For any Zariski dense $\theta$-transverse subgroup $\Gamma$, we introduce  the notion of $\theta$-growth indicators and  discuss their properties and roles in the study of conformal measures,  extending the work of Quint (2003). We also prove that for any $(\Gamma,\psi)$-conformal measure on the $\theta$-boundary,   the conical set of $\Gamma$ has measure either $1$ or $0$, depending on whether the $\psi$-Poincare series  diverges or not; this extends recent works of Sambarino and of Canary-Zhang-Zimmer  proved for special measures supported on the limit set. Our work is new even for $\theta$-Anosov subgroups and answers a question of Sambarino (2022).  Applications include an analogue of the Ahlfors measure conjecture: the limit set of a $\theta$-Anosov subgroup is either the whole boundary or of Lebesgue measure zero. When theta is the set of all simple roots, these were previously obtained by Minju Lee-Oh.

This talk  is based on joint work with Dongryul Kim and Yahui Wang.
September 29, 2023
Friday Morning Seminar Friday Morning Seminar 10:00am -
809 Commons

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!