Previous Conferences & Workshops

We construct an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of Coulomb gas on the unit circle at any given inverse temperature. Our approach combines elements from the theory of orthogonal...

We present a novel tree representation for the hard-core lattice gas model (weighted independent sets) on a general graph. We use this representation to show that for any graph of maximum degree D, the Gibbs measure is unique (the influence of any...

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...

The classification of finite simple groups is widely acknowledged to be one of the major results in modern mathematics. The successful completion of its proof was announced in the early 1980's by Daniel Gorenstein. The original proof occupied...

Random matrices is a large area in mathematics, with connections to many other areas, such as mathematical physics, combinatorics, and theoretical computer sience, to mention a few. There are, by and large, two kinds of random matrices. The first...

We will discuss this model of a random simple path and its connection to spanning trees, matrix formulas, the Potts model and SLE. Time permitting, we shall discuss the proof the it has a scaling limit in three dimensions. No prior knowledge will be...

Perhaps the most appealing conjectures in asymptotic convex geometry are (i) slicing (or isotropic constant) and (ii) variance. Together, they imply that for a random point X from an isotropic convex body in \R^n, the variance of |X|^2 is O(n). We...

Closed subgroups of the automorphism group of a tree which acts locally primitively have a rich structure theory. Combined with superrigidity for irreducible lattices in products of trees such that the projection in each factor is locally primitive...

We introduce a metric space which is the closure of the isomorphism classes of graphs in a natural topology. It turns out that the regularity lemma is equivalent with the compactness of this space. We present applications, open questions, and...

Internal conflict is considered to be a fundamental psychological phenomenon, and many behaviors in both humans and animals have been attributed to it. However, from a biological standpoint, internal conflict is counterintuitive, in that it appears...