Previous Conferences & Workshops

Let $S$ and $T$ be two dense subsets of $G^n$, where $G$ is the special linear group $\mathrm{SL}(2,q)$ for a prime power $q$. If you sample uniformly a tuple $(s_1,\ldots,s_n)$ from $S$ and a tuple $(t_1,\ldots,t_n)$ from $T$ then their interleaved...

In this talk I'll discuss a lattice point count for a thin semigroup inside $\mathrm{SL}_2(\mathbb Z)$. It is important for applications I'll describe that one can perform this count uniformly throughout congruence classes. The approach to counting...

One of the most effective methods for solving boundary value problems for basic elliptic equations of mathematical physics in a given domain is the method of layer potentials. Its essence is to reduce the entire problem to an integral equation on...

In the last few years, there has been a significant interest in the computational abilities of Physarum Polycephalum (a slime mold). This drew from a remarkable experiment which showed that this organism can compute shortest paths in a maze...

In this talk, we discuss our work in progress about how degeneration of the divisor at infinity into a normal crossing divisor affects the symplectic homology of an affine variety. From an anti-surgery picture, by developing an anti-surgery formula...

In this talk I will review CM theory of complex projective K3 surfaces, and show how it can be used to construct K3 surfaces over finite fields. I will discuss work-in-progress where this is applied to describing: (1) the collection of zeta...

The Penrose tiling (Roger Penrose(1974)) and the "quasi-crystal" made by Ron Schactman (1985) are beginning landmarks here. Our objects today are tilings $T$, of $\mathbb R^d$, [$d = 1, 2$ mostly] which like Penrose's is aperiodic and can be a...

Let $R$ be a regular semi-local domain, containing a field. Let $G$ be a reductive group scheme over $R$. We prove that a principal $G$-bundle over $R$ is trivial, if it is trivial over the fraction field of $R$. If the regular semi-local domain $R$...

I will try to tell the story of the projective line minus three points from the point of view of periods, and if time permits, discuss some open problems.