Organizers: Laura Anderson, Vaidy Sivaraman, and Thomas Zaslavsky.

**Tuesday, January 28**

*Speaker*: Dillon Mayhew (Victoria University of Wellington, visiting Princeton)

*Title*: Some Approaches to Characterizing Representable Matroids

*Time*: 1:15 - 2:15

*Room*: LN-2205**Tuesday, February 4**

Organizational meeting

*Time*: 1:15 - 2:15

*Room*: LN-2205**Tuesday, February 11**

*Speaker*: Laura Anderson (Binghamton)

*Title*: Introduction to Matroid Polytopes

*Time*: 1:15 - 2:15

*Room*: LN-2205**Tuesday, February 18**

*Speaker*: Melissa Fuentes (Binghamton)

*Title*: Proper Connection of Graphs

*Time*: 1:15 - 2:15

*Room*: LN-2205**Tuesday, February 25**

*Speaker*: Marcelo Aguiar (Cornell)

*Title*: The Ring of Graphs and the Chromatic Polynomial

*Time*: 1:15 - 2:15

*Room*: LN-2205**Tuesday, March 4**(joint with the Algebra Seminar)

*Speaker*: Luise-Charlotte Kappe (Binghamton)

*Title*: On the Covering Number of Small Symmetric Groups and the Erdös-Ko-Rado Theorem**Tuesday, March 11***Speaker*: Thomas Zaslavsky (Binghamton)*Title*: Geometry and the Chess Pieces*Time*: 1:15 - 2:15*Room*: LN-2205**Tuesday, March 18***Speaker*: Vaidy Sivaraman (Binghamton)*Title*: Important Conjectures and Problems I Like*Time*: 1:15 - 2:15*Room*: LN-2205**Tuesday, March 25***Speaker*: Laura Anderson (Binghamton)*Title*: Positroids? Did you say "Positroids"?*Time*: 1:15 - 2:15*Room*: LN-2205**Tuesday, April 1***Speaker*: Richard Behr (Binghamton)*Title*: An Introduction to Threshold Graphs*Time*: 1:15 - 2:15*Room*: LN-2205Threshold graphs were first introduced by Chvatal and Hammer to distinguish cliques of a graph in a polydedral representation. A threshold graph is a graph G, for which there exist non-negative real weights w

_{v}for each vertex v and a threshold number t, such that for distinct vertices x and y, xy is an edge in G if and only if w_{x}+ w_{y}> t. They are important partly because they are "perfect", but also for other reasons. I will provide and prove several different characterizations of these graphs, as well as discuss properties of randomly generated threshold graphs, which arise very naturally. I will finish up by discussing a new generalization, now under investigation by Vaidy Sivaraman and me.**Tuesday, April 8 (joint with the Geometry/Topology Seminar)***Speaker*: Jay Schweig (Oklahoma State)*Title*: Bounding the Homology of a Simplicial Complex*Time*: 1:15 - 2:15*Room*: LN-2205One of the most basic questions concerning a simplicial complex K is the following: How can we combinatorially construct a bound i such that H

_{j}(K) vanishes for j < i? For any complex K, the minimal nonfaces of K form a clutter (or hypergraph). We show how certain combinatorial invariants of this clutter bound the homology of the complex K, and also how they can be used to study algebraic invariants of K's Stanley-Reisner ideal.

This is joint work with Hailong Dao.**Tuesday, April 15**

Spring Break**Tuesday, April 22***Speaker*: Peter Maceli (Columbia)*Title*: Coloring Graphs with Forbidden Induced Subgraphs*Time*: 1:15 - 2:15*Room*: LN-2205Efficiently coloring an arbitrary graph is a fundamental and notoriously difficult algorithmic problem. This talk focuses on the restricted problem of determining the complexity of coloring graphs which do not contain a certain induced subgraph. This problem remains NP-complete unless the excluded induced subgraph is a disjoint union of paths.

Recently much work has been done on this problem. Only one case remains open if we are allowed to use at least four colors: Determining the complexity of four-coloring graphs with no induced six-vertex path.

The most interesting remaining case is the problem of three-coloring graphs without long induced paths. Maria Chudnovsky, Mingxian Zhong, and I resolved the first open case: three-coloring graphs with no induced seven-vertex path can be done in polynomial time. Juraj Stacho and I have also made progress on the open four-coloring question.

In this talk, I will discuss some of the ideas and the general spirit of these structural coloring algorithms.**Tuesday, April 29***Speaker*:*Title*:*Time*: 1:15 - 2:15*Room*: LN-2205**Tuesday, May 6***Speaker*:*Title*:*Time*: 1:15 - 2:15*Room*: LN-2205**Tuesday, May 13***Speaker*:*Title*:*Time*: 1:15 - 2:15*Room*: LN-2205

*Speaker*: Jim Lawrence (George Mason)

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