MIT-Harvard-MSR Combinatorics Seminar: Vector bundles, valuations, tropical linear spaces and matriods
SEMINARS, HARVARD-MIT COMBINATORICS
Speaker:
Kiumars Kaveh - University of Pittsburgh
Torus equivariant rank r vector bundles on a toric variety (toric vector bundles) were famously classified by Klyachko (1989) using certain combinatorial data of compatible filtrations in an r-dimensional vector space E. This data can be thought of as a higher rank generalization of an (integer-valued) piecewise linear function. In this talk, we give interpretations of Klyachko data in terms of valuations with values in a certain meet-join lattice as well as points on a tropical linear space. Since tropical linear spaces correspond to linear matroids, this point of view leads us to introduce the notion of a "matroidal vector bundle", a generalization of toric vector bundles to general matroids (possibly non-representable). The talk focuses on the combinatorial side of the story and I will give a brief review of toric varieties at the beginning. This is a work in progress with Chris Manon (Kentucky).
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For information about the Combinatorics Seminar, please visit...
http://math.mit.edu/seminars/c
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