Abstracts for BICMR-HCM: Beijing meets Bonn

Dual complex characterizes how components of a divisor intersect each other. We will sketch the recent progress on using minimal model program to study it, with applications in various natural settings.

An axiomatic definition of cohomological field theories (CohFT) was introduced by Kontsevich and Manin. This theory includes Gomov-Witten thoery and quantum singularity theory as special cases. The genus-0 part of a CohFT introduces a Frobenius manifold structure. When the Frobenius manifold is semisimple, the genus-2 potential function can be solved from universal equations or Virasoro constraints. The solution depends on the so called canonical coordinates on the Frobenius manifolds. Recently B. Dubrovin, S. Liu, and Y.

We give a survey on $L^2$-invariants such as $L^2$-Betti numbers and $L^2$-torsion. We describe some of their applications to questions in topology, geometry, group theory and algebra and discuss some open problems.

A time-dependent family of Riemannian manifolds is a super-Ricci flow if $2 Ric + \partial_t g \ge 0.$ This includes all static manifolds of nonnegative Ricci curvature as well as all solutions to the Ricci flow equation. We extend this concept of super-Ricci flows to time-dependent metric measure spaces. In particular, we present characterizations in terms of dynamical convexity of the Boltzmann entropy on the Wasserstein space as well in terms of Wasserstein contraction bounds and gradient estimates. And we prove stability and compactness of super-Ricci flows under mGH-limits.