This mini-symposium will feature the 12th cohort of MLB scholars completing the program this month. Each MLB scholar will give a 25-minute presentation of their research and have 5 minutes to answer questions from the audience.

The MLB mini-symposium will take place on Wednesday, April 24 at 12:00pm in 1068EH. A reception will follow the talks.

Please RSVP here: https://docs.google.com/forms/d/e/1FAIpQLSdreyLUEvil0fyny8JqV5BiSOGsyfUCPLhdAQ3IeITFWy8s6Q/viewform

Speaker: Jordan Grant
Title: A Bridge to Higher Teichmüller Theory
Abstract: Higher Teichmüller Theory can be broadly described as the study of representations of surfaces of negative Euler characteristic $S$ into semisimple lie groups $G$ of rank greater than 2. We study these representations by studying the topology of the representation variety $\text{Hom}(\pi_{1}(S),G)/G$. These representations allow us to parameterize deformations of our surface which correspond to distinct geometric structures. By studying the resulting spaces of representations corresponding to geometric structures, known as Higher Teichmüller spaces, we are able to gain some understanding of the flexibility or rigidity of the geometry of a given surface.

While Higher Teichmüller Theory is a fairly young field, it is heavily motivated by the tools and problems established in the rank 1 case, or classical Teichmüller theory. This talk will serve as a bridge between these two topics, outlining the tools and techniques used to build classical Teichmüller space, and then generalizing these tools to the higher rank case. In the end I will briefly cover some results of Higher Teichmüller Theory, as well as discuss some recently proposed conjectures.

Speaker: Gerardo Dutan
Title: Constructing a Framework for Optimal Player Management
Abstract: One of the crises hitting sports leagues around the world today is the issue of how to protect the entertainment value of their product. Leagues commonly suffer drops in watchability when key stars do not play either from injury or team-enforced resting policies.

In this talk, we propose a modeling framework for addressing load management issues seen in professional sports. Our goal is to adequately characterize the dynamics of a sports league and construct a method for obtaining a well-defined optimal policy for a team to implement. We base our approach on contest theory principles that borrow from game theory and stochastic Markov decision processes.

Speaker: Javier Santiago
Title: On Permutation Polynomials over $\mathbb{F}_{q^2}$ induced by exceptional rational functions
Abstract: In this talk, we will present our approach to the study of permutation polynomials over $\mathbb{F}_{q^2}$, which centers around understanding exceptional rational functions over $\mathbb{F}_q$. In particular, we discuss how to use geometric methods in order to gain insight into said rational functions, and we use such methods to give a classification of exceptional rational functions of small degree. This in turn allows us to produce large numbers of classes of permutation polynomials over $\mathbb{F}_{q^2}$ in a systematic manner.