In-person meetings are held in AP&M 7321 and Zoom meetings are held here.

If you would like to be included or removed from our email announcements, please email Brandon Seward.

If you would like to give a talk, please send the title, abstract and related papers (if available) of your proposed talk to one of the organizers by email.

Organizers: Amir Mohammadi, Anthony Sanchez, Brandon Seward

Fall 2024 Speakers Past Speakers

- Sept. 26:

- Oct. 3:

- Oct. 10: Rodolfo Gutiérrez-Romo (Universidad de Chile)

Location: Zoom

Title: The diagonal flow detects the topology of strata of quadratic differentials

Abstract: A half-translation surface is a collection of polygons on the plane with side identifications by translations or half-turns in such a way that the resulting topological surface is closed and orientable. We also assume that the total Euclidean area of the polygons is finite. Two half-translations are equivalent if a sequence of cut-and-paste operations takes one to the other. From the view of complex geometry, an equivalent definition is a Riemann surface endowed with a meromorphic quadratic differential with poles of order at most one.

A stratum of half-translation surfaces consists of those with prescribed cone angles at the vertices of the polygons. Strata are, in general, not connected. A natural flow, the diagonal or Teichmüller flow, acts on stratum components.

In this talk, we investigate some topological properties of stratum components. We show that the (orbifold) fundamental group of such a component is "detected" by the diagonal flow in that every loop is homotopic to a concatenation of closed geodesics (coned to a base-point). Using this result, we show that the Lyapunov spectrum of the homological action of the diagonal flow is simple, thus establishing the Kontsevichâ€“Zorich conjecture for quadratic differentials.

This is a joint work with Mark Bell, Vincent Delecroix, Vaibhav Gadre, and Saul Schleimer.

- Oct. 17: Sidhanth Raman (UC Irvine)

- Oct. 24: Ben Johnsrude (UCLA)

- Oct. 31:

- Nov. 7: Shreyasi Datta (University of York)

- Nov. 14:

- Nov. 21:

- Dec. 5: Andreas Wieser (UCSD / Institute for Advanced Study)