Matroids seminar: Difference between revisions
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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]. | ||
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<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div> | |||
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<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 19:58, 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 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. |
| 2/8/2019 |
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 |