**Title**: What is Topological Entropy?

**Speaker**: Joshua Yee (Ohio State University)

**Abstract**: This talk will introduce the notion of topological entropy as it appears in Adler, Konheim, and McAndrew's paper. I will briefly cover the terminology relating to open coverings of a topological space used in constructing their definition of entropy. The definition of entropy will then be presented, followed by an explanation of several mathematically useful properties of entropy. The talk will conclude with example computations of entropy and the statement of an alternate definition originating from Dinaburg and Bowen.

- Adler, Konheim, & McAndrew. "Topological Entropy."
*Transactions of the American Mathematical Society*, vol. 114, no. 2 (Feb., 1965), pp. 309-319. - Bowen. "Entropy for Group Endomorphisms and Homogeneous Spaces."
*Transactions of the American Mathematical Society*. vol. 153 (Jan., 1971), pp. 401-414.

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The What is ...? seminar's main goal is to expose culturally ambitious participants to some mathematical notions not taught in standard courses. These topics form an important part of mathematical folklore, and may prove useful for doing research and enhancing teaching. Lectures will be given mostly by graduate and undergraduate student participants. Professors Vitaly Bergelson and Daniel Shapiro serve as coordinators/mediators.

The What is ...? Seminar is an event organized by the Mathematics Department, independent of SAMMS, but participants are encouraged to attend any meeting that seems intriguing! Let the attending mediator know you are a SAMMS participant.