Project Description

Modular categories are intricate organizing algebraic structures appearing in a variety of mathematical subjects. Besides the intrinsic mathematical aesthetics, another motivation for studying modular categories comes from their application in condensed matter physics and quantum computing. There is a notion of dimension associated with these categories and their objects. The idea of this project is to investigate how much we can say about the structure of these categories by imposing some restrictions on the values of these important numbers (the dimensions). We will use algebra and number theoretical techniques together with computational and numerical approaches. 

Technology or Computational Component

The student will develop a simple code to find different sets of numbers (the dimensions mentioned before) that need to satisfy certain conditions. There are different possible coding languages that will serve this project such as mathematica, python, and Matlab among others. The ideal student will be able to write the code after discussing the restrictions with me.