Previous Conferences & Workshops

Studying the covolume of lattices goes back to the work of Siegel in the forties where he shows that $(2,3,7)$-triangular group is a lattice of minimum covolume in $G = \mathrm{SL}_2(\mathbb R)$. The case of $\mathrm{SL}_2(\mathbb C)$ has been open...

The main purpose of the talk is to describe an approach for the estimate of averages over orbits of certain functions on the space of lattices. These estimates play a crucial role in the study of the distribution of values at integral points of...

Let us fix $m$ conjugacy classes $C_1,\dots,C_m$ inside $GL(n)$. The variety of $m$-tuple of matrices such that: $$X_i\in C_i, \quad i=1,\dots,m mbox{ and } X_1\dots X_m=1.$$ is a solution of the Deligne-Simpson problem. Double affine Hecke algebras...

The integer quantum Hall effect (IQHE) entails a very precise quantization of the Hall conductance in a 2D sample at very low temperatures. Depending on whether the currents in the sample are ascribed to the bulk or the edge, two apparently...

In this talk I will prove the following counterpoint to a result by Kashin and Szarek (cf. Theorem 1, C. R. Acad. Sci. Paris, Ser. I, 1336 (2003) 931-936)): There exists a map \phi from infinite-dimensional euclidean space into the space of...

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 shall discuss Quantum Computing, and the so called Hidden Subgroup Problem, which in the abelian case was the basis for Shor's celebrated factorization algorithm. The solution for non-abelian groups, and symmetric groups in particular, is one of...

I will discuss various issues related to the local problem on Lie groups, the asymptotics of the return probablity, and the equidistribution of dense subgroups.

Within non-relativistic quantum electrodnamics, atoms interacting with the radiation field are expected to have a ground state. It is further expected that the ground state exists independently of the size of the coupling constant $\alpha$ and the...