School of Mathematics

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...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Tropical ideals are combinatorial objects that abstract the behavior of the collections of subsets of lattice points that arise as the supports of all polynomials in an ideal. Their structure is governed by a sequence of ‘compatible’ matroids and...

Expressing combinatorial invariants of matroids as intersection numbers on algebraic varieties has become a popular tool in algebraic combinatorics. Several conjectured inequalities among combinatorial data can be traced back to positivity results...

In 2008, looking to bound the face vectors of tropical linear spaces, Speyer introduced the g-invariant of a matroid, defined in terms of exterior powers of tautological bundles on Grassmannians. He proved its coefficients nonnegative for matroids...

Suppose f is a function with Fourier transform supported on the unit sphere in Rd. Elias Stein conjectured in the 1960s that the Lp norm of f is bounded by the Lp norm of its Fourier transform, for any p>2d/(d−1).  We propose to study this...