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.
| Uhrzeit: |
10:30 - 11:30 |
| Ort: |
C4H33 |
| Gruppe: |
Oberseminar kombinatorische algebraische Geometrie |
| Einladender: |
Daniele Agostini, Hannah Markwig |
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.
| Uhrzeit: |
14:00 |
| Ort: |
Hörsaalzentrum N2 |
| Gruppe: |
Oberseminar Algebraische Geometrie |
| Einladender: |
V. Batyrev, J. Hausen, Th. Markwig |
