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
