[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: John Rached

[Cary Malkiewich]

Hi everyone,

A quick reminder about the geometry/topology lunch today (meet outside
WH100E) and John's talk in the seminar today at 2:50pm. See you there!

Cary

On Tue, Sep 5, 2023 at 9:59 AM Cary Malkiewich <
malkiewich at math.binghamton.edu> wrote:

> Hi everyone,
>
> This week we are pleased to have our very own John Rached speaking about
> dynamics on the moduli space of surfaces, 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:* Quantitative behavior of horocycle flow on the moduli space of
> genus 2 surfaces
> *Abstract:* The action of SL(2,R) on moduli space exhibits measure
> rigidity, analogously to Ratner’s theorems for unipotent flows on
> homogeneous spaces, due to the seminal work of Eskin-Mirzakhani. Similar
> results cannot hold for the horocycle flow on moduli space, but for special
> subvarieties of strata (eigenform loci), some key tools from homogeneous
> dynamics have an incarnation in this inhomogeneous setting. A version of
> Ratner’s theorem holds for eigenform loci, and a flurry of recent work on
> quantitative results for actions on homogeneous spaces begs a natural
> question - can one effectivize arguments for the horocycle flow on
> eigenform loci? We give some support for a positive answer to this
> question, and make some conjectures.
>
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