Video Lectures

This will be a talk mostly on wave dark matter - if the dark matter constituent is lighter than about 10 eV, dark matter is best thought of as a set of waves. After a brief introduction, we will discuss two recent ideas that explore the implied wave...

Locally conformally symplectic (LCS) manifolds are manifolds that are symplectic up to a locally defined positive factor. In this generalization, we still have (locally conformally) exact Lagrangians, (locally conformally) Hamiltonian vector fields...

I will discuss the wonderful theory of intersection homology, introduced by Goresky and MacPherson, and its connections to the combinatorics of convex polytopes and cellular spaces. I will mention results and questions about "toric g-vectors"...

A stationary measure in random dynamics is an analog of an invariant measure for a classical dynamical system. While there is no reason, in general, for an invariant measure of a diffeomorphism to have any regularity, it turns out that, under mild...

The generalized Penrose conjecture for initial data sets satisfying the dominant energy condition asserts that the ADM mass is bounded below by a quantity involving the area of the outermost generalized apparent horizon. In this talk, I will discuss...

We present a proof of the Arnold-Givental conjecture on the number of intersection points between the fixed-point set of an anti-symplectic involution and its transverse Hamiltonian image. Our argument combines the methods of integral Floer theory...

Current pulsar timing array (PTA) projects are galactic-scale gravitational-wave (GW) detectors whose sensitivity is approaching the point at which a signal should become clearly detectable. Despite the strong evidence reported in the literature, I...

I will discuss recent progress on a Grassmannian formulation of correlation functions in the large-N O(N) vector model, motivated by higher-spin holography. The formulation leads to a remarkably simple n-point formula and suggests an underlying...

A folklore belief in economics is that "simple auctions" should "perform well" if and only if the auction's participants view the items for sale as substitutes (as opposed to complements). How can this belief be formulated as a precise conjecture...

Given a hypergraph with edges of size at most 3, the 3-set cover problem asks to determine the minimum size of a family of edges that covers the vertex set. As the problem is NP-hard, it is natural to consider its fractional (linear programming)...