### July 23rd: Masha Gordina, University of Connecticut

Title: Emmy Noether, Symmetry and the Calculus of Variations

### July 16th: Kasso Okoudjou, Tufts University

Title: TBA

Abstract:

### July 9th: Sasha Teplyaev, University of Connecticut

Title: Spectral Dimension of the Universe

Abstract:

We know that our usual space-time is four dimensional, but is it the same on a quantum scale? There is a recent physics theory that there is a so called dynamical dimensional reduction in quantum gravity. This talk will describe the basic mechanism for this dimension reduction, and a surprising connection to the talk by Chris Hayes.

### July 2nd: Patricia Alonso-Ruiz, Texas A&M

Title: Fractals are also in the market

Abstract: How does a financial investor decide which trading strategy to apply? Analyzing and classifying financial data is crucial to make a decision. One general classification involves two types of price behaviors: trending or mean-reverting. In the former, increasing (or decreasing) returns will likely lead to further increasing (or decreasing) returns, while in the latter price increases will likely lead to price decreases (or vice versa).

In this talk we will discuss a way to mathematically describe these regimes and discover that fractals play a fundamental role in that description.

### June 25th: Chris Hayes, University of Connecticut

Title: Fractals and Dirichlet forms

Abstract: We will explore some simple examples of fractals, discuss dimensions of self-similar sets and then look at the basic ingredient in doing analysis (calculus) on some fractals: the construction of a self-similar Dirichlet form.

### June 18th: Emily Gunawan, University of Oklahoma

Title: Box-ball systems and Tableaux

Abstract: Box-ball systems give a combinatorial model of a soliton, or solitary wave. We discuss some results obtained by past REU students in this area.

### June 11th: Oleksii Mostovyi, University of Connecticut

Title: Introduction to financial mathematics

Abstract: We introduce some foundational ideas of financial mathematics, including the first and second fundamental theorems of asset pricing.

### June 4th: Luke Rogers, University of Connecticut

Title: Measurement

Abstract: Since its earliest days, mathematics has been used to measure things. Usually so that someone could tax them! But measuring even simple things like the length of a curve in the plane can present many challenges. We will walk through some of the difficulties one might encounter and learn a little about the mathematics that arises from them.