[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Paul Apisa

[Cary Malkiewich]

Hi everyone,

A quick reminder that Paul Apisa (University of Wisconsin) will be speaking
in our seminar today. See you there!

Best,
Cary

On Mon, Oct 30, 2023 at 9:15 AM Cary Malkiewich <
malkiewich at math.binghamton.edu> wrote:

> Hi everyone,
>
> This week we are pleased to have Paul Apisa (University of Wisconsin)
> speaking about orbit closures in moduli space, title and abstract below.
> This will be an in person talk, on Thursday at 2:50pm in WH 100E.
>
> We will also have a lunch social, meet at 12pm just outside WH100E. See
> you there!
>
> Best,
> Cary
>
> =========================================
> *Title:* Hurwitz Spaces, Hecke Actions, and Orbit Closures in Moduli Space
> *Abstract:* The moduli space of Riemann surfaces is a space whose points
> correspond to the ways to endow a surface with a hyperbolic metric or,
> equivalently, complex structure. Geodesic flow on moduli space can be used
> to generate an action of GL(2, R) on its cotangent bundle. While work of
> Eskin, Mirzakhani, Mohammadi, and Filip implies that GL(2, R) orbit
> closures are varieties, the question of which ones occur is wide open.
> Aside from two well-understood constructions (taking loci of branched
> covers and subloci of rank two orbit closures) there are only 3 known
> families of orbit closures: the Bouw-Moller curves, the
> Eskin-McMullen-Mukamel-Wright (EMMW) examples, and 2 sporadic examples.
> Building on ideas of Delecroix-Rueth-Wright, I will describe work showing
> that the Bouw-Moller and EMMW examples can be constructed using just the
> representation theory of finite groups. The main idea is to connect these
> examples to Hurwitz spaces of G-regular covers of the sphere for an
> appropriate finite group G. In the end, I will describe a construction that
> inputs a finite group G and a set of generators satisfying a combinatorial
> condition and outputs a GL(2, R) orbit closure in moduli space.
>
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