Spring 2006

**Thursday 2/2**

Marge Bayer

*4-Polytopes***Thursday 2/9**

Jeremy Martin

*Cyclotomic and Simplicial Matroids*

**Thursday 2/16**

Jeremy Martin

*Cyclotomic and Simplicial Matroids*(continued)**Thursday 2/23**

Jeremy Martin

*Cyclotomic Lattices and Cyclotomic Polytopes*(after M. Beck and S. Hosten)**Thursday 3/2**

Marge Bayer

*Flag Vectors of Polytopes--An Overview*

**Thursday 3/9**

No seminar**Thursday 3/16**

Manoj Kummini

*Edge and facet ideals***Thursday 3/23**

No seminar (Spring Break)

**Thursday 3/30**

Manoj Kummini

*On the Cohen-Macaulay properties of squarefree monomial ideals*(after S. Faridi)**Thursday 4/6**

Manoj Kummini

*More on Simplicial Trees***Thursday 4/13**

Jeremy Martin

*Counting Spanning Trees of Hypercubes*__Abstract:__The Matrix-Tree Theorem can be used to give a simple formula for the number of spanning trees of the n-dimensional hypercube. However, no bijective proof of this formula is known. I'll discuss a more refined version of the formula, proven by Vic Reiner and myself, which we hope will point the way to a bijection.**Thursday 4/20**

Carly Klivans (University of Chicago)

*Generalized Degree Sequences*__Abstract:__Degree sequences of graphs have been thoroughly studied. For example, there are many simple characterizations of when an integer sequence is the degree sequence of a graph and of graphs with "extremal" degree sequences. Notions of generalized degree sequences for higher dimensional simplicial complexes are not as well investigated. I will talk about work in progress on understanding these degree sequences and those classes of complexes which exhibit analogous extremal behavior. This is joint work with Uri Peled and Amitava Bhattacharya.**Thursday 4/27**

Saul Stahl

*Multicolorings of Graphs***Thursday 5/4**

Matthew Morin (University of British Columbia)

*Ribbons, Caterpillars, and the Chromatic Symmetric Function*__Abstract:__We are interested in Stanley's question of whether the chromatic symmetric function distinguishes nonisomorphic trees. Instead of working with trees in general, we simplify to the problem of distinguishing between certain types of caterpillars. Then, using a bijection between ribbon diagrams and caterpillars, we look at what properties of the ribbons appear in the corresponding chromatic symmetric function.**Thursday 5/11**

Lauren Williams (UC Berkeley/Harvard)

*Tableaux combinatorics for the asymmetric exclusion process*__Abstract:__The partially asymmetric excluion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites. Particles may enter the system from the left with probability alpha, and exit from the right with probability beta. The model is partially asymmetric in the sense that the probability of hopping left is q times the probability of hopping right. In this talk, we will describe a surprising connection between the PASEP model and the combinatorics of certain 0-1 tableaux called permutation tableaux. Namely, we prove that in the long time limit, the probability that the PASEP is in a particular configuration tau is a generating function for permutation tableaux of shape lambda(tau), enumerated according to three statistics. The tableaux in question come from total positivity on the Grassmannian (via work of Postnikov).

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Last updated Wed 8/23/06 10:00 PM