## Factors of sparse polynomials: structural results and some algorithms

In this talk, I will discuss a recent result showing that this is in some sense true for multivariate polynomials when the polynomial has each variable appearing only with bounded degree. Our sparsity bound uses techniques from convex geometry, such as the theory of Newton polytopes and an approximate version of the classical Caratheodory's Theorem.

## Coherence, planar boundaries, and the geometry of subgroups

## A mountain pass theorem for minimal hypersurfaces with fixed boundary

## One-relator groups, non-positive immersions and coherence

Abstract: There seems to be an analogy between the classes of fundamental groups of compact 3-manifolds and of one-relator groups. (Indeed, many 3-manifold groups are also one-relator groups.) For instance, Dehn’s Lemma for 3-manifolds (proved by Papakyriakopoulos) can be seen as analogous to Magnus’ Freiheitssatz for one-relator groups. But the analogy is still very incomplete, and since there are deep results on each side that have no analogue on the other, there is a strong incentive to flesh it out.

## On the Approximation Resistance of Balanced Linear Threshold Functions

## The general case?

## Singular Hodge theory of matroids

## Front propagation in a nonlocal reaction-diffusion equation

We consider a reaction-diffusion equation with a nonlocal reaction term. This PDE arises as a model in evolutionary ecology. We study the regularity properties and asymptotic behavior of its solutions.

## A Party for Which People? The Democrats from Andrew Jackson to Barack Obama and Beyond