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

[Cary Malkiewich]

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

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*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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