Video Lectures

Abstract: A highly excited Maass form on a hyperbolic surface is expected to behave like a random monochromatic wave . We will discuss this in connection with the question of the nodal domains of such forms on arithmetic hyperbolic surfaces with a...

Abstract: One of the principles of the endoscopic classification is that if an automorphic representation of a classical group is non-tempered at any place, then it should arise as a transfer from an endoscopic subgroup. One also knows that any...

Abstract: (joint with N.Mok, J.Pila) Shimura varieties (S) are uniformized by symmetric spaces (H), and the uniformization map Pi:H --> S is quite transcendental. Understanding the interaction of this map with the two algebraic structures is of...

Abstract: The Jacquet-Rallis trace formula is a powerful tool to study periods of automorphic forms of unitary groups that show up in Ichino-Ikeda conjecture. In this talk, I will report on the present state of the Jacquet-Rallis trace formula. Then...

Abstract: In work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh we give a new construction of some Eisenstein classes for $GL_N (Z)$ that were first considered by Nori and Sczech. The starting point of this construction is a...

Abstract: In recent joint work with Jan Bruinier, Ben Howard, Michael Rapoport and Tonghai Yang, we proved that a certain generating series for the classes of arithmetic divisors on a regular integral model M of a Shimura variety for a unitary...

Abstract: For a smooth and projective variety X over a global field of dimension n with an adelic polarization, we propose canonical local and global height pairings for two cycles Y, Z of pure dimension p, q satisfying $p+q=n-1$. We will give...

Abstract: This is a work in progress inspired by the the arithmetic Gan--Gross--Prasad conjecture where one is interested in the arithmetic diagonal cycle on the product of two Shimura varieties. We study special cycles on simple Shimura varieties...

Abstract: Relative (or spherical) characters describe the restriction of a representation to a subgroup. They arise naturally in the study of periods of automorphic forms, e.g., in the setting of conjectures of Gan-Gross-Prasad and Ichino-Ikeda....