| 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. |
| 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.
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| 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 |
| 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). |
Links
[1] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/2024-W08
[2] https://calendar.math.yale.edu/list/calendar/grid/week/abstract/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