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

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

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

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

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

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

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

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

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

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