Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Toric degenerations from Tropical Geometry and Representation Theory

Seminar | February 20 | 3:45-5 p.m. | 939 Evans Hall

 Lara Bossinger, University of Cologne

 Department of Mathematics

In this talk I will explain how toric degenerations arise from the tropicalization of a (projective) variety. In the context of varieties that are interesting from a representation theoretic point of view (e.g. Grassmannians or flag varieties) I will explain a construction of toric degenerations due to Fang, Fourier, and Littelmann called birational sequences. I will present many examples and some results on how the two constructions are related. For example, I will present computational results on the tropicalization of the full flag variety for $n=4$ and $5$ and compare the obtained toric degenerations to some classical degenerations from representation theory (string polytopes and the FFLV polytope) that arise in the context of birational sequences.