Seminars Sorted by Series

We use the recent developments of Jacquet in order to obtain an explicit expression for a compact unitary period of certain automorphic form on GL(n) in terms of special values of L-functions. Jacquet obtains a characterization of the image of...

A celebrated result of Waldspurger provides a relation between Fourier coefficients of half-integral weight modular forms and the central value of L-functions of the associated Shimura lift (which is a modular form of integral weight). This has a...

I will discuss the following theme: starting with an a priori Diophantine result (typical flavour: integer solutions to such-and-such equation are well-spaced) and turning it into an equidistribution-type statement on a homogeneous space. This (in...

I will explain a conjectural generalisation of Ihara's lemma in the theory of modular forms to higher dimensional automorphic forms and sketch how this conjecture implies the Sato-Tate conjecture for rational elliptic curves with somewhere...

We will describe some recent ergodic theorems for general families of averages on semisimple Lie groups, and explain how they can be used to 1) Solve the lattice point counting problem for general domains in the group, with explicit estimate of the...

Ideal classes in (totally real) number fields give naturally rise to compact orbits inside SL(n,Z)\SL(n,R) for the diagonal subgroup. We will discuss their (equi-)distribution properties as the field varies, and the two main ideas in our approach...

Given a higher rank arithmetic group (E.g. SL(3,Z)) it has r(n) complex irreducible representations of degree n. We will study the the rate of growth of r(n), the associated zeta function SUM(r(n)n^(-s)), its Euler factorisation etc. Some...

I will describe recent joint work with Janos Pintz and Cem Yildirim on small gaps between primes and primes in tuples. Perhaps the most surprising result is that if the primes have level of distributed in arithmetic progressions greater than 1/2...

We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on compact manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Our results can...

The remarkable phenomenon of Superrigidity, discovered by Margulis in the context of linear representations of lattices in higher rank semi-simple groups, has motivated and inspired a lot of research on other "higher rank" groups and representations...

We consider maps between smooth projective curves and some arithmetic and geometric properties of such maps. In particular, we will discuss the case of maps from the generic Riemann surface of genus g -- a problem first seriously looked at by...

In this talk we will describe two methods which shows that, under some rigidity assumptions on the involved Legendrian submanifolds, a Lagrangian cobordism is simply connected. The first one uses the functoriality of the fundamental class in...

I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya category for contact 1-jet spaces $J^1(X)$. This category is built from Legendrian submanifolds equipped with augmentations...

Satellite operations are a common way to create interesting knot types in the smooth category. It starts with a knot $K$, called the companion knot, in some manifold $M$ and another knot $P$, called the pattern, in $S^1 \times D^2$ and then creates...

In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The main focus is on Weinstein manifolds which admit a Weinstein Lefschetz fibration with an $A_k$-fibre...

In this series of two talks we will discuss Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. The main focus is on Weinstein manifolds which admit a Weinstein Lefschetz fibration with an $A_k$-fibre...

Lagrangian cobordisms between Legendrian submanifolds arise in Relative Symplectic Field Theory. In recent years, there has been much progress on answering qualitative questions such as: For a fixed pair of Legendrians, does there exist a Lagrangian...

Schedule: https://www.ias.edu/math/avi60/agenda