Alternatively have a look at the program.

## Opening/BICMR-HCM: Beijing meets Bonn

## BICMR postdoc program presentation

## Dual complex of pairs

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.

## Small eigenvalues of the Laplacian on surfaces

Eigenvalues of the Laplacian on hyperbolic surfaces are called small, if they lie below $1/4$, the bottom of the spectrum of the Laplacian on the hyperbolic plane. Buser showed that, for any $n \in \mathbb{N}$ and $\epsilon > 0$, the closed surface $S$ of genus $g\ge 2$ carries a hyperbolic metric with $2g - 2$ eigenvalues below $\epsilon$ and $n$ eigenvalues below $1/4 + \epsilon$. Buser's results were refined by Schmutz, and they conjectured that a hyperbolic metric on $S$ has at most $2g - 2$ small eigenvalues.

## Genus-2 generating functions for semisimple cohomological field theory

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.

## BKMP remodeling conjecture and its applications

Mirror symmetry predicts Gromov-Witten theory for a Calabi-Yau manifold from the B-model of its mirror. The BKMP (Bouchard-Klemm-Marino-Pasquetti) remodeling conjecture is a mirror symmetry statement predicting all genus open-closed Gromov-Witten theory for a toric CY 3-orbifold from the topological recursion on its mirror curve. Nice features of the topological recursion as B-model give many desired properties of GW invariants, which are usually difficult to prove by other means. I will sketch a proof of BKMP conjecture and a construction of the global mirror curve over the Kahler moduli.

## Survey on $L^2$-invariants

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.

## HCM presentation

Presentation of the Hausdorff Center for Mathematics, in particular its opportunities for international postdocs.

## Super-Ricci flows of metric measure spaces

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.