Analysis, Spectra and Number Theory, a Conference in Honor of Peter Sarnak’s 61st Birthday

A well-known theorem called the Sylvester-Gallai theorem states that, given n points in R^2, either they all lie on a line or else there is an ordinary line - a line through precisely two of the points. I will discuss joint work with Tao...

In a series of joint papers in 1988-89, Osgood-Phillips-Sarnak identified the extremal metrics of the zeta functional determinant of the Laplacian operator on compact surfaces and applied the result to establish the compactness of isospectral...

In this talk I will overview some of the local and global aspects of the p-adic Langlands program, with an emphasis on explaining and motivating the program and its results to non-experts.

In this talk we will review the recent progress on this conjecture, including Kim-Sarnak/Blomer-Brumley's 7/64 through its automorphic inputs which includes several cases of Langlands functoriality. We will then discuss the conjecture in some...

In the lecture, we will describe several applications of the theory of trace functions (Frobenius trace functions associated to $\ell$-adic sheaves on the affine line over $\mathbb{F}_q$) to analytic number theory. This is a report of several recent...

In this talk I will discuss the asymptotic behaviour of the discrete (resp. cuspidal) spectrum of arithmetic groups with respect to the growth of various parameters such as the level of congruence subgroups, the analytic conductor and the rank of...

This will be primarily a survey talk about recent developments in the area.

In my talk I will survey some of the developments regarding the classification of measures on arithmetic quotients of semisimple groups invariant under diagonalizable subgroups (i.e. tori). I will then considering an application that is not so new...

Ramanujan graphs has been defined and constructed in the 80's by Lubotzky-Phillips-Sarnak and by Margulis. In recent years a high dimensional theory of expanders is emerging and in particular Ramanujan complexes. In the talk we will present a joint...

Quantum ergodicity usually deals with the equidistribution of eigenfunctions of the Laplacian, in the high frequency limit, on a compact Riemannian manifold. Here I will present an attempt to prove a similar theorem on discrete graphs. We consider a...