# Hausdorff Kolloquium 2017

**Date:** May 3 - July 12, 2017

**Venue:** Mathematik-Zentrum, Lipschitz Lecture Hall, Endenicher Allee 60, Bonn

## Wednesday, May 3

## Wednesday, June 21

15:15 |
Gian Michele Graf (ETH Zürich): tba |

16:45 |
Simon Brendle (Columbia University): tba |

## Wednesday, July 12

15:15 |
Tony Yue Yu (CMI and Université Paris-Sud, Orsay): Counting open curves via Berkovich geometry |

16:45 |
Robert L. Pego (Carnegie Mellon University): tba |

## Abstracts:

#### Yves André (IMJ-PRG, Paris): A story about commutative algebra: the direct summand conjecture

We shall give an introduction, from various perspectives, to this classical, elementary-looking conjecture formulated by M. Hochster at the beginning of the 70's. We shall then give a hint on how it was finally solved using ideas and techniques from a completely different domain, far away from the familiar noetherian world of commutative algebra, building upon G. Faltings's almost mathematics and P. Scholze's perfectoid geometry.

#### Laurent Desvillettes (Université Paris Diderot): Coagulation-diffusion equations: how to use results on one dimensional singular parabolic equations for infinite dimensional reaction-diffusion systems

Coagulation-diffusion equations naturally appear in the physics of polymers. They consist in a system of an infinite number of reaction-diffusion equations with infinite sums in the reaction terms.

One of the main issue in this field is the possible appearance of the so-called gelation phenomenon, in which a new phase (the gel) is produced after a finite time. This physical phenomenon corresponds to a blowup in the system of coagulation-diffusion, which can be studied thanks to the duality method and its improvements, devised for one single singular reaction-diffusion equation.

#### Tony Yue Yu (CMI and Université Paris-Sud, Orsay): Counting open curves via Berkovich geometry

Motivated by mirror symmetry, we study the counting of open curves in log Calabi-Yau surfaces. Although we start with a complex surface, the counting is achieved by applying methods from Berkovich geometry (non-archimedean analytic geometry). This gives rise to new geometric invariants inaccessible by classical methods. These invariants satisfy a list of very nice properties and can be computed explicitly. If time permits, I will mention the conjectural wall-crossing formula, relations with the works of Gross-Hacking-Keel and applications towards mirror symmetry.