Past Events

A universal cover in ℝⁿ is a convex set that can cover every set of diameter 1. Lebesgue asked in 1914 what the minimum area of a universal cover in ℝ² is. I shall present my study of the minimum volume V of a universal cover in ℝ³, showing that 0.545 < V < 0.656, improving a previous…

A totally skew embedding of a manifold in Euclidean space is an example of an embedding with extra regularity conditions. For totally skew embeddings, we require the tangent spaces at all distinct points on the manifold to be pairwise skew. I will give a brief history of this problem, discuss…

Fixing integers q,d>2, denote by Q(n,T,B) the ferromagnetic q-Potts measures on graphs G(n), at temperature T>0 and non-negative external field strength B, where as n grows the uniformly sparse G(n) of n vertices converge locally to the infinite d-regular tree. I will review a…

Abstract: An n x n-matrix P is called a projection matrix if P is an idempotent, i.e., P^2 = P; in this context the notion seems anodyne.  If our matrices have coefficients in a more complicated algebraic structure, say a commutative ring R, then the image of a projection matrix is…

We study the renormalization group method and its applications in probability theory.

Abstract: The universal monodromic affine Hecke category is a family of categories over the dual torus. It is obtained by allowing sheaves on the enhanced affine flag variety with arbitrary monodromy along the torus orbits. I will discuss a Langlands dual coherent realization, which is joint…

In this talk I’ll present one of the most fundamental results in Random Matrix Theory: the convergence in distribution of the empirical law of the eigenvalues of a Wigner matrix to the semicircle distribution. This is a classical result dating to the founding of the subject. The proof is…

The refined patchworking theorem (Section 2.5.10–11 of [IMS09])

The classical Calderón problem for the conductivity equation asks if the conductivity of a medium can be determined uniquely by making current and voltage measurements on its boundary. We present an analogous question in the fractional context, called the inverse fractional conductivity problem…

The probability community has obtained fruitful results about the connectivity of random graphs in the last 50 years. Random topology is an emerging field that studies higher-order connectivity of random simplicial complexes, which are higher-order generalizations of graphs. Many classical…