Week of May 2, 2021

May 3, 2021
Group Actions and Dynamics Exponential mixing of 3D Anosov flows Zhiyuan Zhang - University Paris 13 10:15am -
Zoom
Applied Mathematics Linear Multistel Methods for Learning Dynamics Qiang Du - Columbia 1:00pm -
Zoom Meeting ID: 97670014308
May 4, 2021
Geometry & Topology Finite Rigid Sets for Combinatorial Complexes Associated to Surfaces Emily Shinkle - Illinois at Urbana-Champaign 4:00pm -
Zoom

Abstracts

Week of May 2, 2021

May 3, 2021
Group Actions and Dynamics Exponential mixing of 3D Anosov flows 10:15am -
Zoom

We show that a topologically mixing C^\infty Anosov flow on a 3 dimensional compact manifold is exponential mixing with respect to any equilibrium measure with Holder potential. This is a joint work with Masato Tsujii.
Applied Mathematics Linear Multistel Methods for Learning Dynamics 1:00pm -
Zoom Meeting ID: 97670014308

Abstract:  Numerical integration of a given dynamic system can be viewed as a forward problem with the learning of unknown dynamics from available state observations as an inverse problem. The latter has been around in various settings such as model reductions of multiscale processes. It has received particular attention recently in the data-driven modeling via deep/machine learning. The solution of both forward and inverse problems forms the loop of informative and intelligent scientific computing. A naturally related question is whether a good numerical integrator for discretizing prescribed dynamics is also good for discovering unknown dynamics. This lecture presents a study in the context of linear multistep methods.

email tatianna.curtis@yale.edu for info
May 4, 2021
Geometry & Topology Finite Rigid Sets for Combinatorial Complexes Associated to Surfaces 4:00pm -
Zoom

The arc complex and flip graph are simplicial complexes associated to a given surface, each describing combinatorial information about the surface. These complexes were used by Harer in his study of homological properties of the mapping class group, and have connections to Penner’s decorated Teichmuller theory and Fomin-Shapiro-Thurston’s theory of cluster algebras, among others. Irmak-McCarthy, Korkmaz-Papadopoulos, and Aramayona-Koberda-Parlier have shown correspondences between simplicial maps of these complexes and homeomorphisms of the associated surface. The complexes are infinite, but I show that these results can be extended for simplicial maps of certain finite subcomplexes, which we call finite rigid sets.