Combinatorics and Algebra Seminar-When are Tutte polynomials valuatively universal for matroids?

Title: When are Tutte polynomials valuatively universal for matroids?
Speaker: Luis Ferroni, IAS
Date and time: Tuesday 11/12, 10:30am
Place: Phillips 730

Abstract: The G-invariant of matroids, defined by Derksen, exhibits remarkable properties: it serves as a universal valuative invariant for matroids. In particular, since the Tutte polynomial is a linear specialization of Derksen's G-invariant, the Tutte polynomial is also valuative. This leads to a key question: for which classes of matroids do these two invariants convey the same information? In other words, when does the G-invariant become a linear specialization of the Tutte polynomial? For example, if the universe were restricted to uniform matroids, both the G-invariant and the Tutte polynomial would indeed contain the same information. Can we go further? How many additional matroids can be included in the universe while preserving this property? This and further questions will be addressed in this talk.