School of Mathematics

Topology of the Hitchin system has been studied for decades, and interesting connections were found to orbital integrals, non-abelian Hodge theory, mirror symmetry etc. I will explain that a large part of the symmetries in these geometries above are...

Joint work with Amir Mohammadi, Zhiren Wang, and Lei Yang

Let Q be an indefinite ternary quadratic form. In the 1980s Margulis proved the longstanding Oppenheim Conjecture, stating that unless Q is proportional to an integral form, the set of values...

Delta-matroids are "type B" or "type C" analogues of matroids. I will discuss how to extend a geometric construction related to matroids to delta-matroids. Using this construction, we prove the ultra log-concavity of the number of independent sets...

Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Quiver Grassmannians are generalizations of these spaces arise in representation theory as the moduli spaces of quiver subrepresentations. These represent...

The derived category of a variety is an important and difficult invariant. In this talk, I discuss a purely convex-geometric and combinatorial approach to these categories for toric varieties. Along the way, we will run into the curious question of...

Given an anticanonical divisor in a projective variety, one naturally obtains a monotone Kähler manifold, and the divisor complement is naturally a Liouville manifold. For certain kinds of singular divisors, we will outline a result obtaining rigid...

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the...

First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic geometry which allows for the study of Hamiltonian dynamics on a wider range of manifolds while preserving the local...

Delta matroids are a generalization of matroids, encompassing combinatorial structures such as matchings of graphs and principal minors of symmetric matrices. In this talk, I will discuss a notion of valuated Delta matroids and their...

Baker and Bowler (2019) showed that the Grassmannian can be defined over a tract, a field-like structure generalizing both partial fields and hyperfields.

This notion unifies theories for matroids over partial fields, valuated matroids, and oriented...