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

**Tuesday, February 28***Speaker*: Zhexiu Tu (Cornell)*Title*: Topological Representations of Matroids and the**cd**-Index*Time*: 1:15 - 2:15*Room*: WH-100EThere are several different topological representations of non-orientable matroids. In this talk, inspired by Swartz's work, I will show an explicit homotopy sphere arrangement that is a regular CW-complex whose intersection lattice is the geometric lattice of the corresponding matroid. I will also look at enumerative properties, including how the flag f-vector formula of Billera, Ehrenborg, and Readdy for oriented matroids applies to arbitrary matroids.

**Tuesday, March 14**

The seminar is postponed to next week, due to record snowfall.**Tuesday, March 21***Speaker*: Charles Wolf (Rutgers)*Title*: The Polynomial Method and the Finite-Field Kakeya Problem*Time*: 1:15 - 2:15*Room*: WH-100EA finite-field Kakeya set is a subset of (F

_{q})^{n}(the n-dimensional vector space over a finite field of order q) which contains a line in each direction. I will first show how to use polynomials to obtain bounds on the size of a Kakeya set in finite vector spaces. Then I will show how to modify this polynomial technique to obtain better bounds on the size of these Kakeya sets. Time permitting, I will discuss bounds on related incidence problems.**Tuesday, March 28 (joint with the Geometry/Topology Seminar)***Speaker*: Caroline Klivans (Brown)*Title*: On the Connectivity of Three-Dimensional Tilings*Time*: 1:15 - 2:15*Room*: WH-100EI will discuss domino tilings of three-dimensional manifolds. I will focus on the connected components of the space of tilings of such manifolds under local moves. Using topological techniques, I introduce two parameters of tilings: the flux and the twist. The main result characterizes, in terms of these two parameters, when two tilings are connected by local moves. I will not assume any familiarity with the theory of tilings.

**Tuesday, April 4***Speaker*: Chris Eppolito (Binghamton)*Title*:*Time*: 1:15 - 2:15 and 2:50 - 3:50*Room*: WH-100E (1:15) and WH-? (2:50)**Tuesday, April 11**

Holiday!**Tuesday, April 18***Speaker*: Toke Knudsen (Oneonta)*Title*: ?*Time*: 1:15 - 2:15*Room*: WH-100E**Tuesday, April 25***Speaker*: Ringi Kim (Waterloo)*Title*: Coloring Digraphs Containing No Cycles With Two Blocks*Time*: 1:15 - 2:15*Room*: WH-100EA cycle with two blocks c(k,l) is an oriented cycle consisting of two internally disjoint directed paths of lengths at least k and l, respectively, from a vertex to another one. In 2007, Addario-Berry, Havet, and Thomassé asked if every strongly connected digraph D containing no c(k,l) has chromatic number at most k+l−1. In this talk, I show that such a digraph D has chromatic number at most O((k+l)

^{2}), improving the previous upper bound O((k+l)^{4}) of Cohen, Havet, Lochet, and Nisse.This is joint work with Seog-Jin Kim, Jie Ma, and Boram Park.

**Tuesday, May 2***Speaker*: Amelia (Mattern) Cyr (Binghamton)*Title*: ?*Time*: 1:15 - 2:15*Room*: WH-100E**Tuesday, May 9***Speaker*:*Title*:*Time*: 1:15 - 2:15*Room*: WH-100E

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