Events and Activities

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...

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 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...

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...

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...

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...

Rank 1 transformations are a long studied, flexible class of measure preserving transformations. King proved a variety of deep results about rank 1 rank transformations including: A) A rank 1 transformation’s centralizer is the weak closure of its...

The Pila–Zannier strategy has proved to be a particularly fruitful approach: first applied to reprove the Manin–Mumford conjecture, it was later exploited decisively in proofs of the André–Oort conjecture. Crucially relying on a recent counting...

Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of...