Seminars Sorted by Series

Let \(N \geq 3\). In this talk, I will sketch a proof that the ring generated by Eisenstein series of weight \(1\) on the principal congruence subgroup \(\Gamma(N)\) contains all modular forms in weights \(2\) and above. This means that the only...

I will discuss an approach to studying the limiting behavior of automorphic forms on quaternion algebras that succeeds admirably when the levels involved are large squares, and describe some new technical problems that arise in trying to relax this...

I will explain joint work with Kannan Soundararajan, where we find an "L-function analogue" of the Brun-Hooley sieve. Essentially, our method allows us to work analytically with long truncated Euler products inside the critical strip. As a...

We consider level sets of the Gaussian free field on the $d$-dimensional lattice, for $d>2$, above a given real-valued height $h$. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

We consider level sets of the Gaussian free field on the d-dimensional lattice, for d>2, above a given real-valued height h. This defines a percolation model with strong, algebraically decaying correlations. We prove a conjecture of Lebowitz...

Suppose you have a finite group G and you want to study certain related structures (e.g., random walks, Cayley graphs, word maps, etc.). In many cases, this might be done using sums over the characters of G. A serious obstacle in applying these...

Rank gives a natural filtration on representations of classical groups. The eta correspondence provides a clean description of a natural family of representations of a given rank, subject to certain bounds. There is evidence that this construction...

We present a deterministic algorithm for graph connectivity that uses the minimal amount of memory possible, up to a constant factor. Specifically, the algorithm's memory is comparable to that needed to store only a single node of the graph (i.e...

I will explain a very intriguing connection between low dimensional topology, knot invariants, and quantum computation: It turns out that in some well defined sense, quantum computation is _equivalent_ to certain approximations of the Jones...

Huygens' principle (in the narrow Hadamard's sense) for a second-order hyperbolic equation means that its fundamental solution is located on the characteristic conoid. Physically this implies that a localised disturbance will have an effect...

Very recently, J.Y. Welschinger introduced a set of invariants for real varieties that give lower bounds on the number of real algebraic curves satisfying certain incidence relations. After J. Solomon's homological interpretation, these invariants...

We study systems of linear ordinary differential equations dy/dz=A(z)y, where A is a matrix-valued rational function of z. By definition, such equation is rigid if it is uniquely determined by the type of its singularities. Our goal is to provide a...

The notion of Q-operator has been introduced by Baxter as a basic tool to solve quantum integrable systems. We develop Baxter Q-operator formalism for $\mathfrak{g}$-Toda chains for $\mathfrak{g}=\mathfrak{gl}(N,\mathbb{R})$. The constructed Q...

Drinfeld has initiated two geometric approaches to global Langlands conjectures over function fields: one by constructing automorphic sheaves and another one by realizing representations in cohomology of the moduli spaces of F-sheaves (also known as...

In my talk I will describe our joint work with David Kazhdan on the global Langlands correspondence over function fields for arbitrary split reductive groups. Our main result asserts that for every pair $(\pi,\omega)$, where $\pi$ is a cuspidal...

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories $D_n$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element of $SL(2n)$ with two...

This will be a relaxed, very elementary introduction to the central ideas and applications of derived algebraic geometry. My objective is to describe the Artin-Lurie Representability Theorem, and to give a number of interesting examples.

This is the first in a series of (probably) three talks whose goal is to understand Faltings’ paper "A p-adic Simpson correspondence". Roughly speaking, this is a correspondence between Higgs bundles over a smooth proper curve X over the field of p...

The aim of this talk is to introduce some of the technologies used in derived algebraic geometry. Beginning with an explanation of the notion of infinity-groupoid, I will develop the notion of infinity-categories. I will discuss the relationship...

Let G be a reductive algebraic group over a local field k . Hiraga, Ichino and Ikeda have recently proposed a general conjecture for the formal degree of a discrete series representation of G(k) , using special values of the adjoint L-function and...

Spectral properties of random band matrices can be expressed in terms certain statistical mechanics models. Some of these models are generalizations of the Ising model except that the spins belong the the Poincare superdisc and there is...

Spectral properties of random band matrices can be expressed in terms certain statistical mechanics models. Some of these models are generalizations of the Ising model except that the spins belong the the Poincare superdisc and there is...

We will introduce certain operators A(m) on the equivariant cohomology ring of the Laumon quasiflags spaces M_d . The character of A(m) will be equal to the generating function Z(m) of the integrals of the Chern polynomial of the tangent bundle of...

We discuss sharp regularity results for the solutions of the polyharmonic equation in an arbitrary open set. Then we introduce an appropriate notion of capacity which allows to describe the precise correlation between the smoothness of the solution...

We discuss the distribution of the extreme eigenvalues for several classes of large (N X N) Hermitian random matrices. For a class of sparse matrices, the distribution is approximately Tracy--Widom. For band matrices with band width W(N) , the...