Monday, November 7, 2022
Time  Items 

All day 

3pm 
11/07/2022  3:00pm Abstract: In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. This system of hyperbolic nonlinear PDE has served as a playground for all kinds of new problems and methods in PDE analysis and geometry. A major goal in the study of these equations is to investigate the analytic properties and geometries of the solution spacetimes. In particular, fluctuations of the curvature of the spacetime, known as gravitational waves, have been a highly active research topic. In 2015, gravitational waves were observed for the first time by Advanced LIGO (and several times since then). These waves are produced during the mergers of black holes or neutron stars and in corecollapse supernovae. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will talk about the Cauchy problem for the Einstein equations, explain geometricanalytic results on gravitational radiation and the memory effect of gravitational waves, the latter being a permanent change of the spacetime. We will connect the mathematical findings to experiments. I will also address my recent work on various classes of spacetimes producing gravitational waves and what the latter tell us. Location:
AKW 200

4pm 
11/07/2022  4:00pm Given a nonelementary random walk on the isometry group of a Gromov hyperbolic space, we can consider the hitting measure on the Gromov boundary. The regularity of this hitting measure depends on the moment condition on the random walk. In this talk, I will review Benoist and Quint’s approaches to the logregularity of the hitting measure. I will then explain the improvement of this theorem using the recently developed theories of GouĂ«zel and BaikChoiKim. If time allows, I will discussÂ its generalization to other settings, i.e., the CAT(0) visual boundary and the sublinearly Morse boundary. Location:
LOM206
