School of Mathematics

In this talk, I will introduce a class of numerical invariants associated with matrix factorizations, constructed to mirror open Gromov–Witten invariants. Matrix factorizations are algebraic objects expected to correspond, under mirror symmetry, to...

This talk is based on joint work with Naichung Conan Leung. We study the mirror symmetry of nonabelian group actions on symplectic manifolds. We show that the presence of a nonabelian symmetry imposes constraints on non-displaceable Lagrangian...

We prove the quilted Floer cochain complexes form $(A_\infty,n)$ modules over the Fukaya category $Fuk(M \times M^-)$. Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex...

In this talk we discuss the multiplicity question for prime closed orbits of a dynamically convex Reeb flow on the boundary of a $2n$-dimensional star-shaped domain. Our first main result asserts that such a flow has at least n prime closed Reeb...

I will present a (cohomological) Fourier-Mukai transform for tropical Abelian varieties and give some applications, including a (generalized) Poincaré formula (for non-degenerate line bundles on tropical Abelian varieties).

Based on joint work with...

In their recent paper, Giansiracusa and Manaker introduced a notion of tropical subrepresentations of linear representations by considering linear actions on tropical linear spaces. In particular, this framework naturally brings matroids into the...

Given a Morse function on a closed smooth manifold and a Smale gradient-like vector field adapted to it, one can construct a topological category called the flow category associated with this data. Its objects are the critical points of the function...

A valency argument is an elegant and well-known technique for proving impossibility results in distributed computing. It is an example of an extension-based proof, which is modelled as an interaction between a prover and a protocol. Even though...

Tropical geometry is a modern degeneration technique in algebraic geometry. Think of it as a very drastic degeneration in which one associates a limiting object to a family of algebraic varieties that is entirely combinatorial.  I will introduce...

Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate polynomials that...