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
Introduction to matroids
We'll cover the basic definitions and some examples, roughly following these notes.
|1/25/2019 & 2/1/2019||
Algebraic matroids in action
We discuss algebraic matroids and their applications; see Algebraic Matroids in Action.
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
We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following Combinatorial Geometries, Convex Polyhedra, and Schbert Cells.
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.