Members Seminar

Recent Progress on Zimmer's Conjecture

David Fisher
Indiana University, Bloomington; Member, School of Mathematics
December 3, 2018
Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actions of these groups on compact manifolds and in a recent breakthrough with Brown and Hurtado we have proven many of them.

A tale of two conjectures: from Mahler to Viterbo.

Yaron Ostrover
Tel Aviv University; von Neumann Fellow, School of Mathematics
November 19, 2018
In this talk we explain how billiard dynamics can be used to relate a symplectic isoperimetric-type conjecture by Viterbo with an 80-years old open conjecture by Mahler regarding the volume product of convex bodies. The talk is based on a joint work with Shiri Artstein-Avidan and Roman Karasev.

New and old results in the classical theory of minimal and constant mean curvature surfaces in Euclidean 3-space R^3

Bill Meeks
University of Massachusetts Amherst
October 22, 2018
In this talk I will present a survey of some of the famous results and examples in the classical theory of minimal and constant mean curvature surfaces in R^3. The first examples of minimal surfaces were found by Euler (catenoid) around 1741, Muesner (helicoid) around 1746 and Riemann (Riemann minimal examples) around 1860. The classical examples of non-zero constant mean curvature surfaces are the Delaunay surfaces of revolution found in 1841, which include round spheres and cylinders.

Representations of p-adic groups

Jessica Fintzen
University of Michigan
February 26, 2018

I will survey what is known about the construction of (the building blocks of) representations of p-adic groups, mention recent developments, and explain some of the concepts underlying all constructions. In particular, I will introduce filtrations of p-adic groups and indicate some of their remarkable properties.