Previous Conferences & Workshops

In the '80s, Yau conjectured that every closed Riemannian 3-manifold contains infinitely many smooth minimal hypersurfaces. In this talk, I will present a Yau-type existence result for nonlocal minimal surfaces and discuss how one can recover the...

I plan to survey the many ways we have today of constructing expanding Cayley graphs of finite groups, and the ideas behind their analysis (some useful beyond that purpose). I want to highlight that despite a comprehensive understanding of achieving...

Given a compact hyperbolic surface of fixed topology, we consider its Laplace eigenvalues together with the structure constants for multiplication with respect to a suitable orthonormal basis of Laplace eigenforms. These numbers obey algebraic...

We develop the spectral analysis of the Jacobi operator on the interfaces of soap-bubble clusters. By Plateau's laws, these always meet in threes at $120^{\circ}$-angles, and thus naturally interact via 3 linearly independent "conformal" boundary...

Given a cohomology theory, it is sometimes possible to associate to each $X$ a stack $X'$, called the transmutation of $X$, in such a way that the cohomology of $X$ agrees with the coherent cohomology of $X'$. In practice, each cohomology theory has...

Singularities are local properties of algebraic varieties. For example, the solution set of a polynomial in several variables such as $y^2=x^3$ has a singularity at the origin $(0,0)$. In algebra, one often studies singularities through the quotient...

We define and study an extension of the notion of the VC-dimension of a hypergraph and apply it to establish a Tverberg type theorem for unions of convex sets. We also prove a new Radon type theorem for unions of convex sets, settling an open...

Hilbert, motivating his list of 23 problems, mentions the arithmetical formulation of the concept of the continuum in the works of Cauchy, Bolzano and Cantor, and the discovery of non-Euclidean geometry by Gauss, Bolyai and Lobachevsky, as...