# Research

## Discrete Mathematics

### Monday, April 27, 2020

Title: TBA
Speaker: Michael Hendry
Time: 2:00pm‐3:00pm
Place: CMC 108

TBA

### Monday, March 23, 2020

Title: TBA
Speaker: Scott Grizzard
Time: 2:00pm‐3:00pm
Place: CMC 108

TBA

### Monday, March 16, 2020

SPRING BREAK -- no seminar this week.

### Monday, March 9, 2020

No seminar this week.

### Monday, March 2, 2020

Title: Polytopes, Complexes, and Patterns
Speaker: Greg McColm
Time: 2:00pm‐3:00pm
Place: CMC 108

#### Abstract

The usual definition of a pattern is of a family of subsets of some Euclidean space, usually a family preserved under some group of isometries of that space. However, additional structure is often presumed when using patterns in the study of, say, tilings or geometric graphs. We restrict our attention to patterns derived via complexes from polytopes. This talk is largely a reformulation of known definitions and maybe a known result or two.

### Monday, February 24, 2020

Title: The synchronization phase transition: exact results, open problems, and extensions
Speaker: Razvan Teodorescu
Time: 2:00pm‐3:00pm
Place: CMC 108

#### Abstract

The synchronization phase transition is a generic name for a class of dynamical systems describing the evolution of atomic distributions supported on the unit circle, in the limit where the number of point masses becomes infinite. Starting from the original (Kuramoto) model, we review the known results and discuss some of the recent extensions of this model.

### Friday, February 14, 2020

Title: Independence Polynomials and Their Roots
Speaker: Jason Brown, Dalhousie University
Time: 2:00pm‐3:00pm
Place: CMC 108

#### Abstract

Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph $$G$$. In addition to encoding useful information about the graph (such as the number of vertices, the number of edges and the independence number), the analytic and algebraic properties can say much about the shape and inter-dependence of the coefficients. In this talk we will focus on the nature and location of the roots of such polynomials, and even cross paths with a fractal or two! As well, we’ll connect to classical results from the masters of analysis.

### Monday, February 10, 2020

Title: Categories for the Working Crystallographer
Speaker: Greg McColm
Time: 2:00pm‐3:00pm
Place: CMC 108

#### Abstract

Mathematical and theoretical crystallography and materials science enjoys a vast array of models of various materials. We start with an introduction to a class of models and describe some basics for model construction and analysis using tools from category theory. This talk will not presume any prior familiarity with either crystallography or category theory.