Representation Theory
Representation theory is ubiquitous. In simplest terms, it's the art of mapping an abstract object to an anchored framework. Doing this usually reveals information about both the object and the framework. When we apply this to group theory (in my case finite group theory) the abstract is objects are these mathematical objects we call groups and the framework is usually linear algebra. My research on the topic mostly revolved around an invariant of finite groups called the Burnside ring. In a nutsell, the Burnside ring of a finite group is an algebraic object built on the summary of how a group can interact with objects outisde of itself. More information can be sought out in the link to links to my papers below.
If anyone stumbles on this and wants to chat with me further about Burnside rings, feel free to shoot me an email!
Graph Theory
Graphs theory is the mathematical study of networks. My research concerned classifications of graph properties with respect to graph minors. An introduction to the topic of graph minors can be read on Wikipedia (here). A famous example of such a classification is Wagner's Theorem. For more excitement regarding graph minors, I highly recommend reading about the beautiful Robertson-Seymour Theorem.
Current Interests: Combinatorial Game Theory and Reinforcement Learning
A combinatorial game is a turn-based two player game that always ends after a finite number of moves. Additionally, none of the game information is hidden from either player (a non-example of this is the game Battleship). A simple example is Tic-Tac-Toe. Another well known example is the game Nim.
More details coming soon! If you're interested, you can check out the work with my collaborator Charlie Petersen on the game UpDown.
You can find links to much of my research on Google Scholar