## KU Combinatorics Seminar Spring 2015

The Combinatorics Seminar meets on Friday in Snow 408 at 3-4pm.

Please contact Jeremy Martin if you are interested in speaking.

Friday 1/23
Organizational meeting

Friday 1/30
Jeremy Martin
Noncrossing partitions in combinatorics and analysis

Friday 2/6
Bennet Goeckner
Cohen-Macaulay relative simplicial complexes

Friday 2/13
Ken Duna
Eigenvalues of combinatorial Laplacians of matroid complexes

Friday 2/20
Brent Holmes
Diameters of subgraphs of the Johnson graph

Friday 2/27
Jeremy Martin
Tutte polynomials of graphs and Poincaré polynomials of varieties

Friday 3/6
Josh Fenton
Game matching numbers of graphs

Friday 3/13
No seminar (Spring Break)

Friday 3/20
No seminar (Spring Break)

Friday 3/27
Kernels of digraphs, and digraphs from absorbant sets

Friday 4/3
Ghodratollah Aalipour (Kharazmi University, Iran / University of Colorado, Denver)
Some properties of Laplacian eigenvalues of graphs and their possible generalization to simplicial complexes

Abstract: The Laplacian matrix of a graph, and its eigenvalues, have played an important role in many areas of mathematics and computer science such as the theory of random walks and data clustering. In this talk we first review some well-known properties of Laplacian eigenvalues of graphs and their relation to several graph invariants such as the number of spanning trees, diameter, vertex connectivity, and expansion properties. Then we present the corresponding generalization of previous known results for Laplacian eigenvalues of graphs to Laplacian eigenvalues of pure simplicial complexes as uniform hypergraphs. Finally, we deliver some open problems.

Friday 4/10
Jeremy Martin
Shellability, partitionability, and Stanley depth

Friday 4/17
Bennet Goeckner
A non-partitionable Cohen-Macaulay simplicial complex
This talk is about the paper of the same name at arxiv.org/1504.04279.

Friday 4/24
José Alejandro Samper (University of Washington)
Matroidal vs. shifted simplicial complexes

Abstract: We will discuss a program to construct a class of ordered simplicial complexes that generalises matroid independence and pure shifted simplicial complexes and enlightens some of the similarties between these two remarkable classes of complexes. To this end we relax several of the classical matroid axioms such as the exchange and circuit axioms. We motivate such constructions by relating them to two classical problems: a 1977 conjecture of Stanley about the h-vector of a matroid and a question of Reiner and Duval about the similarities of matroidal and shifted complexes. We will present some of the consequences of the two mentioned axioms, like the existence of a well behaved Tutte-polynomial and a well defined nbc complex. We then pose several questions and, if time permits, explain briefly the other axioms we have considered. Based on joint work with Steven Klee.

Friday 5/1
On Kernels, $$\beta$$-graphs, and $$\beta$$-graph Sequences of Digraphs (Master's Project Final Presentation)