Vorträge in der Woche 30.01.2023 bis 05.02.2023

Dienstag, 31.01.2023: Condensed sets II

Claudius Kamp

Mittwoch, 01.02.2023: Kp solitons from tropical limits

Claudia Fevola (MPI Leipzig)

The interplay between algebraic curves and the Kadomtsev-Petviashvili hierarchy establishes a fascinating connection between algebraic geometry and integrable systems. In this talk, we study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. The Riemann theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota variety which parametrizes all tau functions arising from such a sum. The combinatorial structure of the Delaunay polytope is central to describe the defining ideal of the Hirota variety. This is joint work with Daniele Agostini, Yelena Mandelshtam and Bernd Sturmfels.

Donnerstag, 02.02.2023: Topology of toric varieties and a brief introduction to intersection spaces

Shahryar Ghaed Sharaf (Universität Heidelberg)

In this talk, I investigate the topological aspects of toric varieties. I start with the construction of the links of toric varieties. Using the homology groups of links, we show that singular points have similar characterizations from the topological and algebraic geometrical points of view. In the second part of the talk, I introduce the theory of intersection spaces. Finally, I construct the associated intersection spaces to 6-dimensional toric varieties and discuss the obtained results.

Donnerstag, 02.02.2023: The nonlinear stability of Kerr for small angular momentum

Jérémie SZEFTEL (Sorbonne Université, France)

I will introduce the celebrated black hole stability conjecture according to which the Kerr family of metrics are stable as solutions to the Einstein vacuum equations of general relativity. I will then discuss the history of this problem, including a recent work on the resolution of the black hole stability conjecture for small angular momentum.

Freitag, 03.02.2023: Konstruktion von CW-Komplexen aus Sullivan-Algebren mit quadratischem Differential, Teil III

Pascal Zeller (Uni Tübingen)