Difference between revisions of "Matroids seminar"

From UW-Math Wiki
Jump to: navigation, search
Line 12: Line 12:
  
 
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"
 
{| cellpadding="8px" style="vertical-align:top; text-align:left; cellpadding:10px;"
|1/18/2019
+
|3/8/2019
 
|
 
|
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div>
+
<div style="font-weight:bold;">Vladmir Sotirov</div>
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
<div><i>Introduction to matroids</i></div>
+
<div><i>Infinite matroids</i></div>
 
<div class="mw-collapsible-content">
 
<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].
+
TBA
 
</div></div>
 
</div></div>
 
|-
 
|-
|1/25/2019 & 2/1/2019
+
|3/1/2019
 
|
 
|
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div>
+
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div>
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
<div><i>Algebraic matroids in action</i></div>
+
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].
+
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 [https://arxiv.org/abs/1902.03719 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.
 
</div></div>
 
</div></div>
 
|-
 
|-
|2/8/2019
+
|2/22/2019
 
|
 
|
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div>
+
<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 class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div>
+
<div><i>The Kazhdan-Lusztig polynomial of a matroid</i></div>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
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]
+
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 conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers.
 
</div></div>
 
</div></div>
 
|-
 
|-
Line 48: Line 48:
 
</div></div>
 
</div></div>
 
|-
 
|-
|2/22/2019
+
|2/8/2019
 
|
 
|
<div style="font-weight:bold;">[https://www.math.wisc.edu/~wang/ Botong Wang]</div>
+
<div style="font-weight:bold;">[http://www.math.wisc.edu/~csimpson6/ Connor Simpson]</div>
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
 
<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>
+
<div><i>Proving the Heron-Rota-Welsh conjecture</i></div>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
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 conjectures from [https://arxiv.org/pdf/1611.07474.pdf these] [https://arxiv.org/pdf/1412.7408.pdf two] papers.
+
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]
 
</div></div>
 
</div></div>
 
|-
 
|-
|3/1/2019
+
|1/25/2019 & 2/1/2019
 
|
 
|
<div style="font-weight:bold;">[https://math.berkeley.edu/~ceur/ Chris Eur]</div>
+
<div style="font-weight:bold;">[https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez]</div>
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
<div><i>The multivariate Tutte polynomial of a flag matroid</i></div>
+
<div><i>Algebraic matroids in action</i></div>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
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 [https://arxiv.org/abs/1902.03719 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.
+
We discuss algebraic matroids and their applications; see [https://arxiv.org/abs/1809.00865 Algebraic Matroids in Action].
 
</div></div>
 
</div></div>
 
|-
 
|-
|3/8/2019
+
|1/18/2019
 
|
 
|
<div style="font-weight:bold;">Vladmir Sotirov</div>
+
<div style="font-weight:bold;">[https://sites.google.com/site/dcorey2814/home Daniel Corey]</div>
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
 
<div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:450px; overflow:auto;">
<div><i>Infinite matroids</i></div>
+
<div><i>Introduction to matroids</i></div>
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
TBA
+
We'll cover the basic definitions and some examples, roughly following [http://web.ma.utexas.edu/users/sampayne/pdf/Math648Lecture3.pdf these notes].
 
</div></div>
 
</div></div>
 
|-
 
|-
 
|}
 
|}

Revision as of 16:09, 4 March 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

3/8/2019
Vladmir Sotirov
Infinite matroids

TBA

3/1/2019
The multivariate Tutte polynomial of a flag matroid

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.

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 conjectures from these two papers.

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.

2/8/2019
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

1/25/2019 & 2/1/2019
Algebraic matroids in action

We discuss algebraic matroids and their applications; see Algebraic Matroids in Action.

1/18/2019
Introduction to matroids

We'll cover the basic definitions and some examples, roughly following these notes.