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>
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<div><i>Algebraic matroids in action</i></div>
 
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We talk about algebraic matroids, matroid polytopes, and their connection to algebraic geometry.
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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 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 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
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 many conjectures from these two papers.