Video Lectures

we will describe various models of sparse and planar graphs and the associated distributions of eigenvalues (and eigenvalue spacings) which come up. The talk will be light on theorems, and heavy on experimental data.

Let p be an odd prime number and let F be a totally real field. Let F_cyc be the cyclotomic extension of F generated by the roots of unity of order a power of p . From the maximal abelian extension of F_cyc which is unramified (resp. unramified...

Associated to any simplicial graph there is a right-angled Coxeter group. Invariants of the Coxeter group such as its growth series or its weighted L^2 Betti numbers can be computed from the graph's clique complex (i.e., its flag complex).

A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns intersect in at...

In a sequence of recent papers, Sudan and coauthors have investigated the relation between testability of properties of Boolean functions and the invariance of the properties with respect to transformations of the domain. Linear-invariance is...

The systolic inequality says that if we take any metric on an n-dimensional torus with volume 1, then we can find a non-contractible curve in the torus with length at most C(n). A remarkable feature of the inequality is how general it is: it holds...

Fontaine and Mazur have a remarkable conjecture that predicts which (p-adic) Galois representations arise from geometry. In the special case of two dimensional representations with distinct Hodge-Tate weights, they further conjecture that these...

https://www.ias.edu/math/files/seminars/FontaineAbst.pdf