**January 31**: Sam Shepherd

**Title**: The boundary at infinity

**Abstract**: Given a metric space, like the plane, one can imagine points at infinity, with one point at the end of each geodesic ray. Together these points form the boundary at infinity for the space. I will describe several examples of spaces where we can construct the boundary at infinity, and discuss some important properties.

**February 21**: Denali Relles

**Title**: Cantor’s function, or: why derivatives are weird

**Abstract**: In mathematics we love weird things. They let us say, “Why is this weird?” and “What else is weird?” and “Should this be allowed?”. Even in topics you may already know, like derivatives, you have to be careful about the specifics. In this talk, I will talk about a certain function called “Cantor’s Staircase,” and explain why it is weird. Then, I’ll discuss how we deal with this as mathematicians by saying certain things are allowed and certain things aren’t.

**March 7**: Hengrong Du

**Title**: Entropy: how do we measure uncertainty?

**Abstract**: The concept of entropy appears frequently in the physical and mathematical literature. It is often recognized as the entropy function xlogx. In this talk, I will introduce the axioms for measuring uncertainty or disorder and derive the entropy function from those axioms. Furthermore, I will discuss the maximum entropy principle in statistical physics.

**March 28**: Peter Huston

**Title: **Uses of the Perron-Frobenius theorem

**Abstract: **Matrices with only non-negative entries show up frequently in mathematics and in the real world. The Perron-Froebenius theorem shows that the largest eigenvalue of such a matrix is positive, and corresponds to an eigenvector with positive entries. We will examine the geometric reality behind this apparently algebraic result, and see a diverse host of applications in mathematics and other fields.