In Fall 2026, seminar will run Fridays from 2–3 p.m. in Evans 939. Talks are 50 minutes (starting at 2 Berkeley time = 2:10), and there will be ample time for questions afterwards.
Organized by Aaron Calderon, Srivatsav Kunnawalkam Elayavalli, and Amir Mohammadi.
September 4, 2026
Izhar Oppenheim (Ben-Gurion)
Title: Banach Fixed Point Properties of Universal Lattices
Abstract: Higher-rank universal lattices and Steinberg groups over Z[t_1,…,t_m] can be viewed as generalizations of higher-rank algebraic lattices.
In this lecture, I will discuss results showing that these groups possess the fixed point property for all affine isometric actions on uniformly convex Banach spaces. This result provides a far-reaching extension of my earlier work on Banach property (T) for SL(n,Z) that was later generalized by de Laat and de la Salle for all higher rank algebraic lattices.
September 11, 2026
Claire Burrin (Zurich)
Title: Modular systoles are optimal for the crossing number
Abstract: I will show that the family of systoles on congruence surfaces have minimal crossing number. This is work joint with Sebastian Baader, Luca Studer, and Hugo Parlier.
September 18, 2026
Tina Torkaman (UChicago)
Title: Entropy and self-intersection number of geodesic currents on compact hyperbolic surfaces
Abstract: Let X be a compact hyperbolic surface and C a geodesic current which is a geodesic-flow invariant measure. Denote the measure-theoretic entropy of C by h_X(C). In this talk, assuming C is ergodic, we give an upper bound on h_X(C) in terms of its self-intersection number i(C,C) and the systole of X. In particular, we show that a small self-intersection number forces small entropy.
September 25, 2026
Omri Solan (IAS & Princeton)
Title: Horocycle-invariant measures on the moduli space of translation surfaces
Abstract: The group SL_2(R) acts on the moduli space of translation surfaces with volume 1 and genus g. We will discuss an ongoing project of classifying the probability measures on the moduli space that are invariant under the horocycle action. This result extends and is built upon a result of Eskin and Mirzakhani that classifies SL_2(R) invariant measures. We will discuss an application to billiard dynamics and some of the difficulties in the proof.
October 2, 2026
Bram Petri (Jussieu)
Title: Apollonian random manifolds and their bass notes.
Abstract: I will speak about joint work with Will Hide, Anna Roig Sanchis and Joe Thomas. We use a model of random hyperbolic 3-manifolds to investigate the set of all possible spectral gaps of hyperbolic 3-manifolds of finite volume.
October 9, 2026
No seminar
October 16, 2026
No seminar
October 23, 2026
Liyang Shao (Berkeley)
Title: Winning of badly approximable vectors on manifolds
Abstract: Diophantine approximation, the study of approximating vectors by rationals, has long been connected to homogeneous dynamics thanks to Dani. In particular, badly approximable vectors are an interesting object to study due to its smallness in Lebesgue measure, and yet largeness in Hausdorff dimension. In this talk, we will first introduce Dani’s correspondence. Then we will recall how nondivergence estimates from Kleinbock-Margulis can be applied to show the winning property (stronger than full Hausdorff dimension) of badly approximable vectors, in terms of the game first introduced by Schmidt. If time permits, we will go into details about the difficulty of such application on manifolds and how it can be resolved. This is joint work with Shreyasi Datta.
October 30, 2026
Wooyeon Kim (KIAS)
Title: Local statistics of the Laplace spectrum on 3D rectangular flat tori
Abstract: In this talk, we show that the pair correlation of the Laplacian eigenvalues on 3-dimensional rectangular flat tori follows Poissonian statistics. Similar to the earlier work of Eskin, Margulis, and Mozes on 2D flat tori, these eigenvalues are represented by values of positive definite quadratic forms at integer points. In the 3D case, the problem reduces to a special case of the quantitative Oppenheim conjecture for rapidly shrinking intervals. Our approach reformulates the problem in terms of homogeneous dynamics via theta functions on (SL_2(R)/SL_2(Z))^3, and relies on a quantitative estimate for escape of mass in this space. This is joint work with Jens Marklof and Matthew Welsh.
November 6, 2026
Giovanni Forni
Title: TBA
Abstract: TBA
November 13, 2026
Jenya Sapir (Binghamton)
Title: TBA
Abstract: TBA
November 20, 2026
Inga Valentiner-Branth (Ghent)
Title: TBA
Abstract: TBA
November 27, 2026
No seminar: Thanksgiving
December 4, 2026
TBA
December 11, 2026
TBA
