Tuesday, April 20, 2021
Time  Items 

All day 

9am 
04/20/2021  9:00am In the 1980s, PiatetskiShapiro and Rallis discovered a family of RankinSelberg integrals for the classical groups that did not rely on Whittaker models. This is the socalled doubling method. It grew out of Rallis' work on the inner products of theta lifts  the Rallis inner product formula. Recently, a family of global integrals that represent the tensor product Lfunctions for classical groups (joint with Friedberg, Ginzburg, and Kaplan) and the tensor product Lfunctions for covers of symplectic groups (Kaplan) was discovered. These can be viewed as generalizations of the doubling method. In this talk, we explain how to develop the doubling integrals for BrylinskiDeligne extensions of connected classical groups. This gives a family of Eulerian global integrals for this class of nonlinear extensions. Location:
Zoom

10am 
04/20/2021  10:15am Abstract: What are normalized characters (aka character ratios) of finite groups good for? We first discuss some applications, assuming good upper bounds on normalized charactersof simple groups. Then we will describe recent results that produce such character bounds. Location: 
4pm 
04/20/2021  4:00pm It is well known that a pseudoAnosov homeomorphism of a closed hyperbolic surface admits two invariant transverse measured laminations. The singularity properties of those laminations record important dynamical characteristics of the homeomorphism. More generally, the same is true for arbitrary points of the of the Teichmuller space. Recently, the study of the properties of “random” pseudoAnosovs as well as of “random” points in the Thurston boundary, and the properties of the corresponding measured laminations, became an important topic in geometric topology. We undertake a similar study for free group automorphisms and the boundary of the CullerVogtmann Outer space. In that contexts pseudoAnosovs are replaced by the socalled “fully irreducible” automorphisms. Points of the boundary of the Outer space are Rtrees, equipped with (usually highly mixing) isometric free group actions that in various senses generalize measured laminations on surfaces. We discuss the branching properties of "random" automorphisms and "random" (in the sense of harmonic measures) trees in the boundary of the Outer space. The talk is based on joint papers with Catherine Pfaff, Joseph Maher and Samuel Taylor. Location:
https://yale.zoom.us/j/96501374645
