Matroids seminar

The matroids seminar & reading group meets 10:00--10:45 on Fridays in Van Vleck 901 in order to discuss matroids from a variety of viewpoints. In particular, we aim to

• survey open conjectures and recent work in the area
• compute many interesting examples
• discover concrete applications

We are happy to have new leaders of the discussion, and the wide range of topics to which matroids are related mean that each week is a great chance for a new participant to drop in! If you would like to talk but need ideas, see the Matroids seminar/ideas page.

To help develop an inclusive environment, a subset of the organizers will be available before the talk in the ninth floor lounge to informally discuss background material e.g., "What is a variety?", "What is a circuit?", "What is a greedy algorithm?" (this is especially for those coming from an outside area).

Organizers: Colin Crowley, Connor Simpson; Daniel Corey, Jose Israel Rodriguez

1/18/2019	Daniel Corey Introduction to matroids We'll cover the basic definitions and some examples, roughly following these notes.
1/25/2019 & 2/1/2019	Jose Israel Rodriguez Algebraic matroids in action We discuss algebraic matroids and their applications; see Algebraic Matroids in Action.
2/8/2019	Connor Simpson Proving the Heron-Rota-Welsh conjecture We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper Hodge theory for combinatorial geometries
2/15/2019	Colin Crowley Matroid polytopes We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following Combinatorial Geometries, Convex Polyhedra, and Schbert Cells.
2/22/2019	Botong Wang The Kazhdan-Lusztig polynomial of a matroid Classically, Kazdhan-Lusztig polynomials are associated to intervals of the Bruhat poset of a Coxeter group. We will discuss an analogue of Kazdhan-Lusztig polynomials for matroids, including results and conjectures from these two papers.
3/1/2019	Chris Eur The multivariate Tutte polynomial of a flag matroid Flag matroids are combinatorial objects whose relation to ordinary matroids are akin to that of flag varieties to Grassmannians. We define a multivariate Tutte polynomial of a flag matroid, and show that it is Lorentzian in the sense of [Branden-Huh '19]. As a consequence, we obtain a flag matroid generalization of Mason’s conjecture concerning the f-vector of independent subsets of a matroid. This is an on-going joint work with June Huh.