Time

Location

Speaker

Abstract

In the first talk I will describe a few definitions of random topological spaces, and some techniques for understanding their basic properties. We are especially interested in their "homological" properties, i.e. are they connected or not, and how many holes do they have?

In the second talk I will describe some constructions of random groups. (This will include fundamental groups of random spaces described in the first talk.) The main point will be to understand how one might understand the likely properties of these groups in various ranges of parameters, such as hyperbolicity or Kazhdan's property (T).

The talks will be self contained --- I will not assume any prior knowledge of probability, topology, or geometric group theory.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 21208 (with Prof H. Moscovici).