# Difference between revisions of "Matroids seminar"

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<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div> | <div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Rodriguez]</div> | ||

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− | <div><i>Algebraic matroids</i></div> | + | <div><i>Algebraic matroids in action</i></div> |

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− | We | + | We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action]. |

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We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells]. | We outline the original formulation of matroid polytopes as moment polytopes of subvarieties of the Grassmanian, following [http://www.math.ias.edu/~goresky/pdf/combinatorial.jour.pdf Combinatorial Geometries, Convex Polyhedra, and Schbert Cells]. | ||

+ | </div></div> | ||

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+ | |2/22/2019 | ||

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+ | <div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div> | ||

+ | <div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;"> | ||

+ | <div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div> | ||

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+ | 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 many conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers. | ||

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## Revision as of 13:58, 16 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!

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?" (this is especially for those coming from an outside area).

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 |