PATCH mini-conference, Friday, September 21

We have Thomas Koberda (Yale), Eriko Hironaka (Florida State) and Andy Putman (Rice) speaking on things vaguely related to the mapping class group:

2pm:

Speaker Thomas Koberda
Title: The complex of curves for a right-angled Artin group
Abstract: I will discuss an analogue of the curve complex for right-angled Artin groups and describe some of its properties. I will then show how it guides parallel results between the theory of mapping class groups and the theory of right-angled Artin groups. Joint with Sang-hyun Kim.

3:30pm

Speaker: Eriko Hironaka
Title: Small dilatation pseudo-Anosov mapping classes
Abstract: A pseudo-Anosov mapping classes on a compact finite-type oriented surface S has the property that the growth rate of lengths of an essential simple closed curve under iterations of the mapping class is exponential, and the growth rate is independent of the choice of curve and the of the choice of metric. This growth rate is called that dilatation of the mapping class. In this talk, we discuss the problem of describing small dilatation pseudo-Anosov mapping classes, i.e., those such that the dilatation raised to the topological Euler characteristic of the surface is bounded. We describe small dilatation mapping classes in terms of deformations within fibered faces, and give some explicit examples. We finish the talk with a conjecture concerning the “shape” of small dilatation mapping classes.

5pm

Speaker: Andy Putman
Title: Stability in the homology of congruence subgroups
Abstract: I’ll discuss some recent results which uncover new patterns in the homology groups of congruence subgroups of SLn(ℤ) and related groups.

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