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Week of February 25, 2024

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February 26, 2024
Group Actions, Geometry and Dynamics [3] Restrictions on Anosov subgroups of some semisimple Lie groups Subhadip Dey - Yale 4:00pm -
KT205
February 28, 2024
Applied Mathematics [4] Modeling and simulating flows in living cells Michael Shelley - NYU 3:00pm -
LOM 214
Colloquium [5] Convergence of unitary representations and spectral gaps Michael Magee - Durham Univeristy and IAS 4:00pm -
KT 219
February 29, 2024
Analysis [6] INTERNAL WAVES IN A 2D AQUARIUM Zhenhao Li - M.I.T 4:00pm -
March 1, 2024
Friday Morning Seminar [7] Friday Morning Seminar 10:00am -
KT801
Applied Mathematics [4] Advances in Biorhythm Deciphering: Time-Frequency Analysis and Statistical Inference Hau-Tieng Wu - NYU 2:00pm -
LOM 214

Abstracts

Week of February 25, 2024

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February 26, 2024
Group Actions, Geometry and Dynamics [3] Restrictions on Anosov subgroups of some semisimple Lie groups 4:00pm -
KT205

Anosov groups constitute a rich class of discrete subgroups of Lie groups, offering both geometric and dynamical intricacies. This class of discrete groups also have deep connections with several current developments in mathematics, such as higher Teichmüller theory and thin groups. For a semisimple Lie group G, each conjugacy class of parabolic subgroups P of G gives rise to a family of Anosov subgroups known as P-Anosov. A natural inquiry is: Which abstract groups can arise as P-Anosov subgroups of G? In this talk, we will discuss some results that fully address this question for many specific pairs of G and P. This talk will be partly based on joint work with Z. Greenberg and J.M. Riestenberg.

February 28, 2024
Applied Mathematics [4] Modeling and simulating flows in living cells 3:00pm -
LOM 214

The insides of cells are geometrically complex, heterogeneous, and dynamic.  Flows inside of cells can reflect the motion of internal structures, and so can be signatures of how forces transduce to motion, or can be an intrinsic part of a self-organizing process involving other moving parts like biopolymers and molecular motors. I’ll show examples of each, discuss the mathematical models that we’ve developed to describe them, and outline the numerical methods we use to simulate them. 

Colloquium [5] Convergence of unitary representations and spectral gaps 4:00pm -
KT 219
Let G be an infinite discrete group. Finite dimensional unitary representations of G in fixed dimension are usually quite hard to understand. However, there are interesting notions of convergence of such representations as the dimension tends to infinity. One notion — strong convergence — is of interest both from the point of view of G alone but also through recently realized applications to spectral gaps of locally symmetric spaces. For example, this notion bypasses (unconditionally) the use of Selberg’s Eigenvalue Conjecture in obtaining existence of large area hyperbolic surfaces with near-optimal spectral gaps.
February 29, 2024
Analysis [6] INTERNAL WAVES IN A 2D AQUARIUM 4:00pm -

Internal waves describe perturbations of a stable-stratified fluid. In an effectively 2D aquarium $\Omega \subset \mathbb{R}^2$, internal waves can be modeled by the equation
$$
(\partial_t^2 \Delta + \partial_{x_2}^2)u(x, t) = f(x) \cos(\lambda t), \quad t \ge 0, \quad x \in \Omega
$$
with Dirichlet boundary and homogeneous initial conditions. The behavior of the equation is intimately related to the underlying classical dynamics, and Dyatlov--Wang--Zworski proved that for $\Omega$ with smooth boundary, strong singularities form along the periodic trajectories of the underlying dynamics. Such phenomenon was first experimentally observed in 1997 by Maas--Lam in an aquarium with corners. We will discuss some recent work proving that corners contribute additional mild singularities that propagate according to the dynamics, matching the experimental observations.

March 1, 2024
Friday Morning Seminar [7] Friday Morning Seminar 10:00am -
KT801

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!

Applied Mathematics [4] Advances in Biorhythm Deciphering: Time-Frequency Analysis and Statistical Inference 2:00pm -
LOM 214

In this presentation, I will explore recent advancements in decomposing intricate biorhythmic time series utilizing time-frequency analysis coupled with statistical inference using a nonlinear time-frequency analysis technique known as Synchrosqueezing Transform (SST). Its motivation and application to digital health will be provided. If time permits, I will advocate the necessity of reconsidering what phase is with these refined tools, and discuss its potential application in patients with chronic obstructive pulmonary disease (COPD).

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Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/2024-W08 [2] https://calendar.math.yale.edu/list/calendar/grid/week/2024-W10 [3] https://calendar.math.yale.edu/seminars/group-actions-geometry-and-dynamics [4] https://calendar.math.yale.edu/seminars/applied-mathematics [5] https://calendar.math.yale.edu/seminars/colloquium [6] https://calendar.math.yale.edu/seminars/analysis [7] https://calendar.math.yale.edu/seminars/friday-morning-seminar [8] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2024-W08 [9] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2024-W10