Video Lectures

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)...

Recent cosmological data hint at a neutrino mass sum below the minimum value physically allowed by neutrino oscillations, with a preference for the opposite of massive neutrinos. Within ΛCDM, Planck CMB, ACT+Planck+SPT CMB lensing and DESI DR2 BAO...

Since their inception, random graphs have been a central topic in probability and combinatorics, offering a remarkably rich landscape for studying how complex structures emerge from randomness. We will discuss the following fundamental questions...

The van der Waerden number w(k;r) is the minimum positive integer N such that every r-coloring of the positive integers up to N contains a monochromatic k-term arithmetic progression. Estimating these numbers has remained a challenging open problem...