Toric Vector Bundles and the tropical geometry of piecewise-linear functions

Algebra Seminar
Monday, March 2, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Chris Manon – University of Kentucky – christopher.manon@uky.edu
Yoav Len

Like toric varieties, toric vector bundles are a rich class of algebraic varieties that can be described with combinatorial data.  Klyachko gave a classification of toric vector bundles in terms of certain systems of filtrations in a vector space.  I'll talk about some recent work with Kiumars Kaveh showing that Klyachko's data has an interesting interpretation in terms of tropical geometry.  In particular, we show that toric vector bundles can be classified by points on tropicalized linear spaces over a semifield of piecewise-linear functions.   I'll discuss how to use this recipe and a closely related tropicalization map to produce toric vector bundles and more general flat toric families.