Video Lectures

We present new objects called quilts of alternating sign matrices with respect to two given posets. Quilts generalize several commonly used concepts in mathematics. For example, the rank function on submatrices of a matrix gives rise to a quilt with...

We present a new method to solve algorithmic and combinatorial problems by (1) reducing them to bounding the maximum, over x in {-1, 1}^n, of homogeneous degree-q multilinear polynomials, and then (2) bounding the maximum value attained by these...

For a smooth projective variety, the classical Hirzebruch--Riemann--Roch (HRR) theorem asserts the isomorphism between the Chow ring and the Grothendieck K-ring of vector bundles over rational coefficients. For certain toric varieties, we show an...

There has been a lot of recent work connecting the two pipe dream formulae for Schubert polynomials (classic and bumpless). One strand is the hybrid pipe dreams of Udell and myself, giving 2n

different pipe dream formulae; an orthogonal one is the...

Chow rings of toric varieties feature a rich combinatorial structure of independent interest. We will begin by surveying four different ways of computing in these rings, due to Billera, Brion, Fulton–Sturmfels, and Allermann–Rau. We will illustrate...

The recent breakthrough of Limaye, Srinivasan and Tavenas (LST) gave the first super-polynomial lower bounds against low-depth algebraic circuits, for any field of zero (or sufficiently large) characteristic. It was an open question to extend this...

I will survey new results on several enumerative problems related to the geometry, topology, and arithmetic of moduli spaces of smooth and stable curves. The enumerative problems include counting isomorphism classes of curves of genus g over a...

In this talk, I will construct an S1-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, I will construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co...

The (small) quantum connection is one of the simplest objects built out of Gromov-Witten theory, yet it gives rise to a repertoire of rich and important questions such as the Gamma conjectures and the Dubrovin conjectures. There is a very basic...

The rectangular peg problem, an extension of the square peg problem, is easy to outline but challenging to prove through elementary methods. In this talk, I discuss how to show the existence and a generic multiplicity result assuming the Jordan...