# 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, ACGT Coordinator.

# Schedule Spring 2016

Note that talks are listed in reverse chronological order.

### A $q$-Queens Problem

**Dates:** 4/26

**Speaker:** Christopher R. H. Hanusa (Queens College, CUNY)

**Abstract:** The $n$-Queens Problem asks in how many ways you can place n queens on an $n\times n$ chessboard so that no two attack each other. There has been no formula for the answer to this question…until now! We develop a mathematical theory to address the more general question “In how many ways can you place $q$ chess pieces on a polygonal chessboard so that no two pieces attack each other?” The theory is geometrical and combinatorial in nature and involves counting lattice points that avoid certain hyperplanes. This is joint work with Thomas Zaslavsky and Seth Chaiken.

### What are the Praeger-Xu graphs, Why are they hated and feared, and What problems about them *can* be solved?

**Dates:** 3/22, 3/29, 4/5, 4/12, 4/19

**Speaker:** Steve Wilson (NAU-Emeritus)

**Abstract:** We study symmetry, in nature, in art, in continuous and discrete objects, because things which have a lot of symmetry are pretty. The more symmetry they have, the prettier they are. Mostly. We will describe a family of graphs, discovered (or created) by Cheryl Praeger and Ming-Yao Xu in 1989, which, because of ‘local’ symmetries, have absurdly large symmetry groups. They have so much symmetry that computer work is helpless for determining most of their properties. We will describe certain properties which *can* be extracted from the tangle. With care.

### Exploration of leading coefficients of Kazhdan-Lusztig polynomials over type affine $C$ Coxeter groups

**Dates:** 2/23, 3/1, 3/8

**Speaker:** Kevin Salmon (NAU)

**Abstract:** In this series of talks, I will summarize the work I’ve done for my MS thesis involving the computation of the leading coefficients for the so-called Kazhdan-Lusztig polynomials in Hecke algebras of type affine $C$.

### Milnor fibers of arrangements in $\mathbb{C}^3$

**Dates:** 1/26, 2/2, 2/9, 2/16

**Speaker:** Michael Falk (NAU)

**Abstract:** In a series of three or four lectures, we will outline a proof that the first homology of the Milnor fiber of a complex 3-arrangement is determined by the intersection lattice, resolving an old conjecture. In the first couple of lectures we’ll lay the groundwork with a quick trip through 3-manifold topology, Seifert manifolds, plumbing, and equivariant resolution of weighted homogeneous singularities, in the special case of interest.