Previous Conferences & Workshops

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have...

For the Obstacle Problem involving a convex fully nonlinear elliptic operator, we show that the singular set of the free boundary stratifies. The top stratum is locally covered by a $C^{1,\alpha}$-manifold, and the lower strata are covered by $C^{1...

I will report on a joint work with M. Abouzaid, S. Guillermou and T. Kragh. The nearby Lagrangian conjecture predicts that a closed exact Lagrangian submanifold in a cotangent bundle must be Hamiltonian isotopic to the zero-section. In particular...

The PCP theorem says that any mathematical proof can be written in a special "PCP" format such that it can be verified, with arbitrarily high probability, by sampling only a few symbols in the proof. Hence the name, Probabilistically Checkable...

I will introduce an isoperimetric inequality for the Hamming cube and some of its applications. The applications include a “stability” version of Harper’s edge-isoperimetric inequality, which was first proved by Friedgut, Kalai and Naor for half...

I will discuss the extreme eigenvalue distributions of adjacency matrices of sparse random graphs, in particular the Erd{\H o}s-R{\'e}nyi graphs $G(N,p)$ and the random $d$-regular graphs. For Erd{\H o}s-R{\'e}nyi graphs, there is a crossover in the...

The study of random matrix moments of moments has connections to number theory, combinatorics, and log-correlated fields. Our results give the leading order of these functions for integer moments parameters by exploiting connections with Gelfand...

Let Q be a non-degenerate indefinite quadratic form in d variables. In the mid 80's, Margulis proved the Oppenheim conjecture, which states that if d ≥ 3 and Q is not proportional to a rational form then Q takes values arbitrarily close to zero at...