# Difference between revisions of "Matroids seminar"

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<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div> | <div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div> | ||

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− | <div><i> | + | <div><i>The multivariate Tutte polynomial of a flag matroid</i></div> |

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− | + | 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. | |

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## Revision as of 22:58, 24 February 2019

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 |
Introduction to matroidsWe'll cover the basic definitions and some examples, roughly following these notes. |

1/25/2019 & 2/1/2019 |
Algebraic matroids in actionWe discuss algebraic matroids and their applications; see Algebraic Matroids in Action. |

2/8/2019 |
Proving the Heron-Rota-Welsh conjectureWe 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 polytopesWe 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 | |

3/1/2019 |
The multivariate Tutte polynomial of a flag matroidFlag 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. |