Video Lectures

I will describe a new lower bound on the number of intersection points of a Lagrangian pair, in the exact setting, using Steenrod squares on Lagrangian Floer cohomology which are defined via a Floer homotopy type.

In contact geometry, a systolic inequality aims to give a uniform upper bound on the shortest period of a periodic Reeb orbit for contact forms with fixed volume on a given manifold. This generalizes a well-studied notion in Riemannian geometry. It...

Quantum Steenrod operations are deformations of classical Steenrod operations on mod p cohomology defined by counts of genus 0 holomorphic curves with a p-fold symmetry, for a prime p. We explain their relationship with the p-curvature of the...

In a landmark paper in 1992, Stanley developed the foundations of what is now known as the Kazhdan--Lusztig--Stanley (KLS) theory. To each kernel in a graded poset, he associates special functions called KLS polynomials. This unifies and puts a...

We heard last week in Daoji's talk about positroid varieties, which are subvarieties in the Grassmannian defined by cyclic rank conditions, and which are related to Schubert varieties. In this talk, we will provide a criterion for whether positroid...

I will discuss the occurrence of some notions and results from contact topology in the context of equilibrium and non-equilibrium thermodynamics. Based on joint works with Michael Entov and Lenya Ryzhik.

In this talk we will discuss some recent progress on some questions in extremal combinatorics and in multiparty communication complexity.

We will also discuss some general connections between the two fields, emphasizing how certain problems (e.g...

In the search for simple, solvable models of quantum cosmology it is useful to focus on general relativity in 2+1 dimensions, where - due to the absence of local degrees of freedom - there is some hope that we can say something precise.  I will...

In 2023, Raghu Meka and I proved a substantially improved bound on the size of the smallest set of integers in [N] which contains no 3-term arithmetic progression. Since then, it has become clear that the main new ideas from that work are in fact...

In this talk I will first define the space of h-cobordisms associated to a manifold M. This space is known to have many non-trivial homotopy groups and in stable range (they can often be computed using Waldhausen's algebraic K-theory of spaces). I...