Euler characteristics of K-classes for pairs of matroids

Abstract: In his 2005 PhD thesis on tropical linear spaces, Speyer conjectured an upper bound on the number of interior faces in a matroid base polytope subdivision of a hypersimplex. This conjecture can be reduced to determining the sign of the Euler characteristic of a certain matroid class in the K-theory of the permutohedral variety. In a recent joint work with Alex Fink, we prove Speyer's conjecture by showing that the requisite Euler characteristic is non-positive for all matroids, and extend this to a statement about pairs of matroids on the same ground set. In this talk, I will provide an overview of our strategy and zoom in on how we extend geometric results for realizable pairs of matroids to all pairs.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca