Talk

I will report on recent results of Hide-Magee, Anantharaman-Monk, Hide-Macera-Thomas proving that random hyperbolic surfaces of large genus have near optimal spectral gap. I will mention results from random graph theory that inspired much of the work on surfaces, and I will try to highlight some ideas from the works mentioned above.

Topological recursion is a powerful tool in mathematical physics with pplications to various problems in enumerative geometry, including intersection theory on moduli spaces and Hurwitz numbers. In this talk, I will discuss the KP integrability of topological recursion, which arises naturally in the context of the x-y swap relation. I will explain how this KP integrability can be described via certain integral transforms, leading to Kontsevich-type matrix models.
 

We prove that if X, Y are derived equivalent complex K3 surfaces, then the integral Chow motives are typically not isomorphic, but are always stably isomorphic. This unfies the result of Huybrechts for isomorphism of rational Chow motives with the result of Mukai for the stable equivalence of integral Hodge structures. Under some mild assumptions, the same result holds for K3 surfaces over nonclosed fields of characteristic zero. For the proofs we rely on known results about zero-cycles on K3 surfaces and set up the machinery of Tate-stable equivalence for integral Chow motives.