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Mathematics & Statistics

# Discrete Mathematics (Leader: Prof. Greg McColm)

## Thursday, September 14, 2000

Title
Speaker
Time
Place

Turing's Famous Leopards' Spots Problem
W. Richard Stark
12:00pm-1:00pm
PHY 108

## Thursday, September 28, 2000

Title
Speaker
Time
Place

Turing's Famous Leopards' Spots Problem, Part II
W. Richard Stark
12:00pm-1:00pm
PHY 108

## Thursday, October 6, 2000

Title
Speaker
Time
Place

Turing's Famous Leopards' Spots Problem, Part III
W. Richard Stark
12:00pm-1:00pm
PHY 108

## Thursday, October 19, 2000

Title
Speaker
Time
Place

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

Topological Entropy of Shift Spaces, Part II
Jamie Oberste-Vorth
12:00pm-1:00pm
PHY 108

## Thursday, November 2, 2000

Title
Speaker
Time
Place

The Rigidity Question for Coxeter Groups
Anton Kaul
12:00pm-1:00pm
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
Speaker
Time
Place

The Rigidity Question for Coxeter Groups, Part II
Anton Kaul
12:00pm-1:00pm
PHY 108

## Thursday, November 16, 2000

Title
Speaker
Time
Place

The Rigidity Question for Coxeter Groups, Part III
Anton Kaul
12:00pm-1:00pm
PHY 108

## Thursday, November 30, 2000

Title
Time
Place

Discrete Mathematics Program Development
12:00pm-1:00pm
First Watch Restaurant

## Thursday, December 7, 2000

Title
Time
Place

Discrete Mathematics Program Development, Part II
12:00pm-1:00pm
PHY 108