UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 04, 2020

939 Evans Hall

3:45PM: Primary Ideals and Differential Equations

Bernd Sturmfels

An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in this context. We characterize primary ideals in terms of PDE, punctual Hilbert schemes, and the join construction, and we present an explicit algorithm for computing Noetherian operators. This is joint work with Yairon Cid-Ruiz and Roser Homs.

5:00PM: K-theoretic Tutte polynomials of morphisms of matroids

Chris Eur

The Tutte polynomial is among the most important combinatorial invariants of a graph and more generally of a matroid. A geometric interpretation of the Tutte polynomial was given by Fink and Speyer via the K-theory of Grassmannians. In this talk, we define and study the Tutte polynomial of morphisms of graphs and matroids by considering the K-theory of flag varieties. We show that there are two natural ways to generalize of the Tutte polynomial in this setting: One of them recovers what is previously known as the Las Vergnas Tutte polynomial, and the other leads to an invariant that remains combinatorially mysterious, save for some first properties we discuss. This is joint work with Rodica Dinu and Tim Seynnaeve.

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