School of Mathematics

I will give an introduction to the microlocal theory of sheaves after Kashiwara and Schapira, and some of its recent applications in symplectic topology. I'll start with the basics, but target applications for the 75 minutes are Tamarkin's proof of...

The "cap set problem" asks for the size of the largest subset $S$ of the vector space $\mathbb F_3^n$ containing no three elements summing to 0. Progress on this problem was slow for many years, until the spring of 2016, when a very short argument...

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open...

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open...

Let $P:\{0,1\}^k \to \{0,1\}$ be a $k$-ary predicate. A random instance of a constraint satisfaction problem (CSP(P)) where each of the $\Delta n$ constraints is $P$ applied to $k$ literals on $n$ variables chosen at random is unsatisfiable with...

The Fukaya category of a symplectic manifold is a robust intersection theory of its Lagrangian submanifolds. Over the past decade, ideas emerging from Wehrheim--Woodward's theory of quilts have suggested a method for producing maps between the...

The motivating question for this talk is: What does a sparse Erdős–Rényi random graph, conditioned to have twice the number of triangles than the expected number, typically look like? Motivated by this question, In 2014, Chatterjee and Dembo...

Of interest are (i) the conjecture of Bombieri (and Lang) that for any smooth projective surface $X$ of general type over a number field $k$, the set $X(k)$, of $k$-rational points is not Zariski dense, and (ii) the conjecture of Lang that $X(k)$...

We show that for constraint satisfaction problems (CSPs), sub-exponential size linear programming relaxations are as powerful as $n^{\Omega(1)}$-rounds of the Sherali-Adams linear programming hierarchy. As a corollary, we obtain sub-exponential size...