Printer-friendly versionAbstracts
Week of September 24, 2023
| Applied Mathematics | Two Techniques Involving High-Dimensional Data |
3:00pm -
LOM 214
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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 |
| Graduate Learning Seminar | Learning seminar on D-modules |
4:00pm -
Prospect 204, B-02
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This is the third lecture in the seminar. |
| Group Actions, Geometry and Dynamics | Growth indicators and conformal measures for transverse subgroups. |
4:00pm -
KT801
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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. |
| Friday Morning Seminar | Friday Morning Seminar |
10:00am -
809 Commons
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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! |