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Location:
Rice University, Herman Brown Hall 227
Date:
January 24th, 2026
Schedule:
9am: Coffee and light refreshments in 4th Floor Lounge (HBH 438)
9:30am: Aaron Brown (Northwestern University)
Title: Absolute continuity and Lyapunov rigidity of stationary measures
Abstract: We consider stationary measures for dissipative (but close to conservative) random walks on surfaces. Assuming sufficient exponential growth and randomness of unstable directions, we show the stationary measures are either finite or absolutely continuous. For perturbations of certain linear systems, we establish certain rigidity of the Lyapunov exponents rigidity showing the exponent decrease unless the system is affine
11am: Chris Lutsko (University of Houston)
Title: Diffusion in random Lorentz models
Abstract: The Lorentz gas is an early model for the motion of electrons through metals and an early model of diffusion. We consider a cloud of non-interacting point particles moving through the compliment of an infinite array of obstacles in $\R^n$. While this model is simple in that the point particles do not interact with one another, in practice even this simple model is not fully understood depending on the obstacle configuration and interaction between point particles and obstacles. A holy grail in this field is to prove an invariance principle in the limit as the time goes to infinity. While this holy grail remains out of reach, I will present joint work with Balint Toth concerning a major step in that direction in a variety of contexts.
12pm: Lunch
2pm: Paul Apisa (University of Wisconsin - Madison)
Title: Moduli spaces of connections, counting problems, and k-differentials.
Abstract: A k-differential (resp. abelian differential) is a flat metric on a surface with finitely many cone points and whose holonomy is a discrete (resp. trivial) subgroup of the circle. The moduli space of k-differential is stratified by specifying the cone angles of the cone points. For abelian differentials, Kontsevich and Zorich classified components of strata and Kontsevich conjectured that they are K(pi, 1). I will describe work in progress with Juliet Aygun, which, using totally different techniques, classifies components of strata of k-differentials and then, in separate work, with Bainbridge and Wang, that makes partial progress on the K(pi, 1) problem. I will then describe applications of new-ish techniques for studying dynamics on moduli spaces that uses this classification to count geodesics on k-differentials. This connects to rational billiards and involves answering a higher-genus version of a problem posed by Mirzakhani and Wright about orbit closures in Teichmuller dynamics.
Parking:
If you are driving, please park in the North Annex Lot. You will have to use a credit card to enter the lot, but can pick up a voucher during the conference to exit for free. Vouchers can be picked up during the coffee break or lunch from Lisa Geda. The North Annex Lot is located at: https://maps.app.goo.gl/Q4riR3PXnSmUQvdr5
Organizing committee:
Some photos from the event:
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