UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 20, 2018

939 Evans Hall

3:45PM: Toric degenerations from Tropical Geometry and Representation Theory

Lara Bossinger

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.

5:00PM: Projective bundles and their Chow rings

Justin Chen

We give a gentle introduction to projective bundles, and explicitly describe their Chow rings (as we will see, this is closely related to the Chern classes as previously introduced). We will see how this allows us to describe Chow rings of interesting varieties, such as blowups along linear spaces.

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