Previous Conferences & Workshops

I will report on joint work with Andrew Lee, which explores the notion that spaces of stable pairs over Riemann surfaces (in the sense of Bradlow and Thaddeus) could form a natural home for a “non-abelian” analog of Heegaard Floer homology for 3...

Given an abelian scheme over a smooth curve over a number field, we can associate two height function: the fiberwise defined Neron-Tate height and a height function on the base curve. For any irreducible subvariety $X$ of this abelian scheme, we...

Given a fibration of compact symplectic manifolds and an induced fibration of Lagrangians, one can ask if we can compute the Floer cohomology of the total Lagrangian from information about the base and fiber Lagrangians. The primary example that we...

We'll discuss how dimensional reductions of the Haydys-Witten equations are connected to Haydys's definition of the Fukaya-Seidel category. Time permitting we'll touch on connections to Donaldson-Thomas's vision of higher-dimensional gauge theory.

Let $F$ be a field of characteristic not equal to 2. Let $r$ be a 2-dimensional even Galois representation which is induced from an $F$-valued character of odd order of the absolute Galois group of a real quadratic field $K$. After imposing some...

Motivated by the goal of establishing a "symplectic sum formula" in symplectic field theory, we will discuss the intersection behavior between punctured pseudoholomorphic curves and symplectic hypersurfaces in a symplectization. In particular we...

A polygon with rational angles can be unfolded and glued into a finite genus Riemann surface equipped with a flat metric and some singularities. The moduli space of all such structures carries an action of the group $\mathrm{PSL}(2,\mathbb R)$ and...

I'll first introduce the Markoff-Hurwitz equation and explain how it plays a fundamental role in different areas of mathematics. The main result I'll discuss is a true asymptotic formula for the number of real points in a fixed orbit of the...