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Mathematics & Statistics

(Leader: Prof. Greg McColm)

**Title**

**Speaker**

**Time**

**Place**

Turing's Famous Leopards' Spots Problem

W. Richard Stark

12:00pm-1:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

Turing's Famous Leopards' Spots Problem, Part II

W. Richard Stark

12:00pm-1:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

Turing's Famous Leopards' Spots Problem, Part III

W. Richard Stark

12:00pm-1:00pm

PHY 108

**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.

**Title**

**Speaker**

**Time**

**Place**

Topological Entropy of Shift Spaces, Part II

Jamie Oberste-Vorth

12:00pm-1:00pm

PHY 108

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**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 \(S'\)).

**Title**

**Speaker**

**Time**

**Place**

The Rigidity Question for Coxeter Groups, Part II

Anton Kaul

12:00pm-1:00pm

PHY 108

**Title**

**Speaker**

**Time**

**Place**

The Rigidity Question for Coxeter Groups, Part III

Anton Kaul

12:00pm-1:00pm

PHY 108

**Title**

**Time**

**Place**

Discrete Mathematics Program Development

12:00pm-1:00pm

First Watch Restaurant

**Title**

**Time**

**Place**

Discrete Mathematics Program Development, Part II

12:00pm-1:00pm

PHY 108