Algebraic and enumerative combinatorics seminar-Alex Fink
Title:The external activity complex of a pair of matroids
| Speaker | Alex Fink |
| Affiliation | Queen Mary University of London |
| Location | MC 5479 |
Abstract: In 2016, Ardila and Boocher were investigating the variety obtained by taking the closure of a linear space within A^n in its compactification (P^1)^n; later work named this the "matroid Schubert variety". Its Gröbner degenerations led them to define, and study the commutative algebra of, the _external activity complex_ of a matroid. If the matroid is on n elements, this is a complex on 2n vertices whose facets encode the external activity of bases.
In recent work with Andy Berget on Speyer's g-invariant, we required a generalisation of the definition of external activity where the input was a pair of matroids on the same ground set. We generalise many of the results of Ardila--Boocher to this setting. Time permitting, I'll also present the tropical intersection theory machinery we use to understand the external activity complex of a pair.
For those who attended my talk at this year's CAAC on this paper, the content of the present talk is meant to be complementary.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm,