Difference between revisions of "Matroids seminar"

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|1/18/2019
 
|1/18/2019
 
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<div style="font-weight:bold;">Daniel Corey</div>
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<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div>
 
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<div><i>Introduction to matroids</i></div>
 
<div><i>Introduction to matroids</i></div>
 
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<div class="mw-collapsible-content">
 
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].
 
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].
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|1/25/2019 & 2/1/2019
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<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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We talk about algebraic matroids, matroid polytopes, and their connection to algebraic geometry.
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|2/8/2019
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<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div>
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<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
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<div><i>Proving the Heron-Rota-Welsh conjecture</i></div>
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We outline the proof of the Heron-Rota-Welsh conjecture given by Adiprasito, Huh, and Katz in their paper [https://arxiv.org/abs/1511.02888 Hodge theory for combinatorial geometries]
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|2/15/2019
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<div style="font-weight:bold;">Colin Crowley</div>
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<div><i>Matroid polytopes</i></div>
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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].
 
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Revision as of 13:47, 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

We talk about algebraic matroids, matroid polytopes, and their connection to algebraic geometry.

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.