Graduate Center, CUNY

Fridays 11:30 am - 12:30 am Room 8405

This seminar covers a wide range of topics in combinatorics and its applications to other disciplines, especially computer science.

The CUNY Graduate Center is located at 365 Fifth Avenue (at the corner of 34th Street), New York. It can be easily approached by subway, using the B,D,F,N,Q,R, or 6 trains.

Seminar organizers are Jonathan Cutler, Christopher Hanusa, Sandra Kingan, and Kerry Ojakian.

Fall 2012 Talks

September 28, 2012: Peter Nelson (Victoria University of Wellington, New Zealand)

Title: The Erdos-Stone Theorem for finite geometries
Abstract: For any class of graphs, the growth function h(n) of the class is defined to be the maximum number of edges in a graph in the class on n vertices. The Erdos-Stone Theorem remarkably states that, for any class of graphs that is closed under taking subgraphs, the asymptotic behaviour of h(n) can (almost) be precisely determined just by the minimum chromatic number of a graph not in the class. I will present a surprising version of this theorem for finite geometries, obtained in joint work with Jim Geelen. This result is a corollary of the famous Density Hales-Jewett Theorem of Furstenberg and Katznelson.

October 5, 2012: No Talk

October 12, 2012:
10:30 am: Jozsef Balogh (University of Illinois)
Title: Independent sets in hypergraphs.
Abstract

11:30 am: Gyula Katona, (Rényi Institute, Budapest, Hungary)
Title: Forbidden intersection patterns in the families of subsets
Abstract

October 19, 2012: Alexander Ellis (Columbia University)

Title: Odd symmetric functions and odd categori ed quantum sl(2)
Abstract: The odd symmetric functions are a Hopf superalgebra that, while neither commutative nor cocommutative, admits combinatorial structure similar to that of the usual symmetric functions. We introduce "odd" analogues of the the nilHecke algebra, the cohomology of Grassmannians, and related algebras. These algebras are used in constructing an odd categori fication of quantum sl(2) and, conjecturally, odd Khovanov homology.

October 26, 2012: John Engbers (University of Notre Dame)

Title: Extremal questions for H-colorings of graphs
Abstract

November 2, 2012: No talk

November 9, 2012: Ezra Halleck (New York City College of Technology, CUNY)

Title: Bijection of two coin flipping events using lattice paths
Abstract: A probability textbook states “An astute student noticed that, in our simulation of the game of heads or tails the proportion of times the player is always in the lead is very close to the proportion of times that the player's total winnings end up 0.” If the number of coins flipped is fixed at $2n$, the size of the events is the central binomial coefficient $\binom{2n,n}$. I will present a bijection between the associated lattice paths as well as generating function techniques used for more general lattice path enumeration.

November 16, 2012: Luis Serrano (Université du Québec à Montréal)

Title: k-Schur functions and dual graded graphs.
Abstract: The k-Schur functions are an important family of symmetric functions which appear in the study of Macdonald polynomials, and the affine Grassmannian, among others. In this talk we will introduce them from the point of view of Fomin dual graded graphs. We also show a more general family of k-Schur functions in the affine nilCoxeter algebra called strong Schur functions, and we prove some properties of them, previously conjectured by Lapointe, Lam, Morse, and Shimozono. This can be found in arxiv:1112.4460, arxiv:1203.4465, and arxiv:1208.4857

November 23, 2012: Thanksgiving break

November 30, 2012: No Talk

December 7, 2012: No Talk

December 14, 2012: Gary Gordon (Lafayette College)

Matroids, greedoids and the Tutte polynomial
Abstract: The Tutte polynomial is a two-variable generalization of the chromatic polynomial of a graph. There are a surprising number of interesting evaluations of this polynomial, which can be defined (in increasing generality) for graphs, matroids or greedoids. In this talk, I will give a survey of some of these applications along with a gentle introduction to matroids and greedoids. Some of this is joint work with Liz McMahon.