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Fakultät für Mathematik

Karlsruher Institut für Technologie
D-76128 Karlsruhe
Tel.: +49 721 608-43800

Toric degenerations in Representation Theory

Referent: Prof. Dr. Ghislain Fourier
Ort: SR 1.067 (20.30)
Termin: 13.12.2016, 13:30 - 14:30 Uhr
Gastgeber: JProf. Dr. Petra Schwer

Zusammenfassung

I'll explain in the talk how Representation Theory provides toric degenerations of spherical varieties, such as flag and Schubert varieties. We will see that a toric degeneration is roughly speaking a simplified translation of a projective variety to a polytope, and hence to Discrete Mathematics. The somehow brute force way to construct such degenerations is via Tropical Geometry, as a running example we work with the Grassmannian of planes.

But this talk will be mainly about the approach using Representation Theory, e.g. canonical bases and Standard Monomial Theory. I'll present a uniform construction that covers all the recent developments in this approach.

There are (conjectured or expected) connections to the approaches using Cluster Theory and Potentials as well as Valuations and Newton-Okounkov bodies.



Ab 14:30 Uhr findet in Raum 1.058 im Kollegiengebäude Mathematik (Geb. 20.30) ein gemeinsamer Tee statt. Herzliche Einladung!