Previous Conferences & Workshops

A much studied combinatorial object associated to a polytope is its "Ehrhart function". This is typically studied for integral or rational polytopes. The first part of the talk will be about joint work with Li and Stanley extending this theory to...

All 3-manifolds can be decomposed into two simple objects, or handlebodies. Some manifolds have many such decompositions, which are distinct. All, however, are related by the operation of stabilization and destabilization. Given two decompositions...

Thurston's hyperbolization of fibered 3-manifolds is based on his classification theorem for isotopy classes of surface homeomorphisms. This classification has also been extremely important to the study of dynamical systems on surfaces. The...

Proof complexity studies the complexity of mathematical proofs, with the aim of exhibiting (true) statements whose proofs are always necessarily long. One well-known proof system is Hilbert's Nullstellensatz, which shows that if the family $F=\{f_1...

I will survey some characterization results on random walks which stick to a small region unusually long. In application we give a description of unitary matrices of large permanent.

We compare absolute and relative Gromov-Witten invariants with the basic contact vector for very positive divisors. For such divisors, one might expect that these invariants are the same up to a natural multiple. We show that this is indeed the case...

Based on a new decoupling inequality for curves in $\mathbb R^d$, we obtain the essentially optimal form of Vinogradov's mean value theorem in all dimensions (the case $d = 3$ is due to T. Wooley). Various consequences will be mentioned and we will...