Topology minicourses

Rachel Skipper (University of Utah, USA)
Title: Groups acting on (rooted) trees

Abstract: In this minicourse, we will explore the world of groups acting on (rooted) trees. Our motivating example will be that of the (first) Grigorchuk group, Γ, first introduced by Rostislav Grigorchuk in 1980.

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J.D. Quigley (University of Virginia, USA)

Title: The realization problem for cohomology rings of classifying space

Abstract: Classifying topological spaces up to homotopy equivalence, or up to continuous deformation, is a fundamental problem in mathematics. The main idea of algebraic topology is to distinguish topological spaces by looking at their associated cohomology rings: if two spaces have non-isomorphic cohomology rings, then they cannot be homotopy equivalent. This minicourse will be concerned with the cohomology rings of classifying spaces, whose computation can be made purely algebraic and algorithmic. After developing the basic theory and working through some examples, we will turn to the realization problem: which rings can be realized as the cohomology rings of topological spaces? We will discuss some classical results and discuss methods for approaching the realization problem for cohomology rings of classifying spaces.

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Francesco Fournier-Facio (University of Cambridge, UK)

Title: Thompson's group F

Abstract: In unpublished notes from 1960, Richard Thompson defined the three groups F < T < V, which act respectively on the interval, circle and Cantor set. Their definition might appear very specific, but these groups have an incredibly rich theory, bizarre combinations of properties, intricate dynamics, and many mysteries surrounding them. I will focus on F, and the long-standing open question of whether it is amenable or not. My hope is that by the end of this minicourse, you will have a new group in your personal library of favourite groups, and a better appreciation of just how strange some groups can be.