# Research

## Discrete Mathematics

### Thursday, September 14, 2000

Title: Turing's Famous Leopards' Spots Problem
Speaker: W. Richard Stark
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, September 28, 2000

Title: Turing's Famous Leopards' Spots Problem, Part II
Speaker: W. Richard Stark
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, October 6, 2000

Title: Turing's Famous Leopards' Spots Problem, Part III
Speaker: W. Richard Stark
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, October 19, 2000

Title: Topological Entropy of Shift Spaces
Speaker: Jamie Oberste-Vorth
Time: 12:00pm‐1:00pm
Place: PHY 108

#### Abstract

In this talk I'll present the definition of entropy for compact metrizable spaces then prove a theorem which enables the entropy to be more easily computed for shift spaces over the integers. Then I'll expand the theorem to include shift spaces over $$Z\times Z$$. Finally, I'll include some information about the entropy of shift spaces over some other groups.

### Thursday, October 26, 2000

Title: Topological Entropy of Shift Spaces, Part II
Speaker: Jamie Oberste-Vorth
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, November 2, 2000

Title: The Rigidity Question for Coxeter Groups
Speaker: Anton Kaul
Time: 12:00pm‐1:00pm
Place: PHY 108

#### Abstract

Coxeter groups are often defined as those having a presentation in which generators have order 2 and all other relations involve only pairs of generators. From a geometric standpoint it is preferable to define Coxeter groups as those that act “by reflections” on some topological space. It turns out that these two definitions are equivalent.

We will discuss the basic definitions and results on Coxeter groups, focusing on the geometric aspects. In particular we will see that any Coxeter group acts by isometries on a complete $$\mathrm{CAT}(0)$$ space (i.e., a metric space of non-positive curvature in the sense of Gromov) called the Davis complex.

The geometry of the Davis complex facilitates a topological approach to the “rigidity question” for Coxeter groups (a Coxeter group $$W$$ is rigid if, given any two generating sets $$S$$ and $$S'$$ for $$W$$, there is an automorphism of $$W$$ which carries $$S$$ to $$S'$$).

### Thursday, November 9, 2000

Title: The Rigidity Question for Coxeter Groups, Part II
Speaker: Anton Kaul
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, November 16, 2000

Title: The Rigidity Question for Coxeter Groups, Part III
Speaker: Anton Kaul
Time: 12:00pm‐1:00pm
Place: PHY 108

### Thursday, November 30, 2000

Title: Discrete Mathematics Program Development
Time: 12:00pm‐1:00pm
Place: First Watch Restaurant

### Thursday, December 7, 2000

Title: Discrete Mathematics Program Development, Part II
Time: 12:00pm‐1:00pm
Place: PHY 108