| Abstract: | Matroids are one of the central notions in
modern combinatorics. They simultaneously generalize the notion of
linear independence in a vector space, and the notion of a graph. One
of the most important matroid invariants is the Tutte polynomial.
In this talk, I will review a geometric interpretation of the Tutte
polynomial based on the K-theory of Grassmannians, and introduce a
natural generalization to so-called flag matroids. For matroids, the
Tutte polynomial is defined combinatorially, and the K-theoretic
interpretation is a property. In contrast, for flag matroids, our
K-theoretic description serves as a definition for the Tutte
polynomial. I will end the talk by discussing some combinatorial
properties of this flag-geometric Tutte polynomial.
This talk is based on joint work with Rodica Dinu and Chris Eur. |
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