# Upcoming Events

Complexity theory is an interesting subject. I will show you the fastest¹ algorithm for any² problem, as well as how to compute anything³ using only three bits of memory.⁴ If time permits, I will explain why these are (at least somewhat) useful.

A fundamental problem in the arithmetic of varieties over global fields is to determine whether they have a rational point. As a first effective step, one can check that a variety has local points for each place. However, this is not enough, as many classes of varieties are known to…

In this talk, I will explain how to use (relative) recursion relations in the HOMFLYPT-skein to study skein-valued open Gromov-Witten partition functions as defined by Ekholm and Shende. As a first application, I will prove a crossing formula for partition functions of basic holomorphic disks…

While unimodal probability distributions are well understood in dimension 1, the same cannot be said in high dimension without imposing stronger conditions such as log-concavity. I will explain a new approach to proving confinement (e.g., variance upper bounds) for high-dimensional unimodal…

Abstract: Compressible Euler solutions develop jump discontinuities known as shocks. However, physical shocks are not, strictly speaking, discontinuous. Rather, they exhibit an internal structure which, in certain regimes, can be represented by a smooth function, the shock profile. We…

Given a four-manifold with non-vanishing Seiberg-Witten invariants, the adjunction inequality provides a lower bound on the genus of any smoothly embedded surface representing a fixed homology class. Stabilization (that is, taking a connected sum with a product of two 2-spheres) always kills the…

We report on recent and on-going work joint with Joerg Bruedern concerning problems involving the representation of integer sequences by sums of powers. Our new tool is an upper bound for moments of smooth Weyl sums restricted to wide major arcs. This permits progress to be made on Waring's…

Abstract

Consider the incidence graph between the points of the unit square and the set of δ x 1 tubes for some δ > 0. What is the size n = n(δ) of the largest induced matching in this graph? We use ideas from projection theory to study this problem and show a non-trivial upper bound on n(δ). As a…

The moduli space M_g of genus g curves (or Riemann surfaces) is a central object of study in algebraic geometry. Its cohomology is important in many fields. For example, the cohomology of M_g is the same as the cohomology of the mapping class group, and is also related to spaces of modular forms…