Chromatic polynomials of tensors and cohomology of complete forms

Abstract: There are two plane quadrics passing through four general points and tangent to one general line. There are six ways to properly color vertices of a triangle with three colors. The maximum likelihood function for a general linear concentration two dimensional model in a four dimensional space has three critical points. Each of these examples of course comes naturally in families. In our talk we will try to explain what the above numbers mean, how to compute them and that they are all shadows of the same construction. Our methods are based on the cohomology ring of the so-called variety of complete forms. The talk is based on works with Conner, Dinu, Manivel, Monin, Seynnaeve, Wisniewski and Vodicka. These are on the other hand based on fundamental works due to Huh, Pragacz, Sturmfels, Teissier, Uhler and others (Schubert included).

algebraic geometrynumber theory

Audience: researchers in the topic

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