# ACGT Seminar

The Algebra, Combinatorics, Geometry, and Topology (ACGT) Seminar meets on Tuesdays at 12:45-2:00pm in Room 164 of the Adel Mathematics Building. If you are interested/willing to give a talk, please contact Dana C. Ernst or Michael Falk, ACGT Co-coordinators.

# Schedule Spring 2018

Note that talks are listed in reverse chronological order.

### Modules, fields of definition, and the Culler-Shalen norm

Date: 3/6/18

Speaker: Charlie Katerba (Montana State University)

### Weak maps of matroids and higher resonance

Date: 2/27/18

Speaker: Mike Falk (NAU)

### Structure of braid graphs for reduced words in Coxeter groups

Dates: 2/13/18, 2/21/18

Speaker: Dana Ernst (NAU)

Abstract: Every element $w$ of a Coxeter group $W$ can be written as an expression in the generators, and if the number of generators in an expression (including multiplicity) is minimal, we say that the expression is reduced. Every pair of reduced expressions for the same group element are related by a sequence of commutations and so-called braid moves. We say that two reduced expressions are braid equivalent if they are related by a sequence of braid moves. Given a reduced expression $\overline{w}$ for a group element $w$, we can form the corresponding braid graph whose vertices are the reduced expressions that are braid equivalent to $\overline{w}$ and two reduced expressions are connected by an edge if there is a single braid move that converts one reduced expression into the other. In this talk, we will describe the overall structure of braid graphs for reduced expressions in Coxeter groups of type $A$ and $B$ in terms of products of graphs.