Fall 2013

The Combinatorics Seminar meets on Fridays, 3-4 PM, in Snow 408.

Please contact Jeremy Martin if you are interested in speaking.

**Friday 8/30**

Organizational meeting

**Friday 9/6**

Jeremy Martin

*Critical and cocritical groups*

__Abstract:__
The critical group of a graph is an abelian group whose order is the number
of spanning trees. It can be constructed algebraically from the Laplacian
matrix and is related to chip-firing, Riemann-Roch theory on graphs. I will
give a broad overview of what is known and unknown about critical groups, and
talk about a dual construction called the cocritical group, which is simpler
for some graphs and harder for others.

**Friday 9/13**

Alex Lazar

The Generalized Towers of Hanoi Problem

**Friday 9/20**

Jeremy Martin

*Generating functions for spanning trees of hypercubes and threshold graphs (warmup for Bernardi's talk)*

**Friday 9/27**

Olivier Bernardi (Brandeis University)

*Symmetries in trees*

__Abstract:__
In this talk, I will present two problems related to the enumeration
of trees. First, I will present a counting formula for multitype
Cayley trees. This formula extends and unifies certain recent results
of Bousquet-Melou and Chapuy. It has application to the multivariate
Lagrange inversion formula and to the study of the profile of random
trees. Second, I will present a combinatorial proof of a counting
formula for the spanning trees of the hypercube. It highlights an
unexpected independence property for the directions of edges in the
uniform spanning tree of the hypercube.

Our proofs for both problems takes advantage of certain symmetries of the enumerative formulas: we first prove these symmetries by simple combinatorial arguments, and then deduce the general formulas from particular cases.

**Friday 10/4**

TBA

**Friday 10/11**

Logan Godkin

*The Sylvester-Gallai Theorem*

**Friday 10/18**

No seminar (St. Louis AMS meeting)

**Friday 10/25**

Jeremy Martin

*Grassmannians, flag varieties and Schubert calculus, part 1*

**Friday 11/1**

*Grassmannians, flag varieties and Schubert calculus, part 2*

**Friday 11/8**

Jeremy Martin

*Pictures of graphs*

**Friday 11/15**

Billy Sanders

*Letter Place Theory*

**Friday 11/22**

Nitin Aggarwal

*Geometry of Wachspress Surfaces*

**Friday 11/29**

No seminar (Thanksgiving)

**Friday 12/6**

Math 996 final presentations

**Friday 12/13**

Math 996 final presentations

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Spring 2007 | Fall 2006 | Spring 2006

Last updated Mon 11/18/13