Joint IAS/PU Groups and Dynamics Seminar

In this talk, we discuss recent developments of geometric methods to classify (infinite) invariant measures in various settings, homogeneous and non-homogeneous. We then discuss new counting results for objects on hyperbolic surfaces. This is joint...

In their resolution of the 3D Kakeya conjecture, Wang and Zahl studied collections of tubes satisfying Convex Wolff axioms. I will discuss a variant of their approach, giving a simpler argument in 3D and that can be extended to collections of convex...

A classical problem in harmonic analysis is to understand how the mass of Laplace eigenfunctions distributes as their parameters tend to infinity. In this talk, I will consider this problem on arithmetic hyperbolic surfaces obtained as quotients of...

How many closed geodesics with length less than $L$ are there on a hyperbolic surface? Classical results of Huber and Margulis say that the counting function has asymptotics $\frac{e^{L}}{L}$. When one is concerned with closed geodesics of a fixed...