Classifying small modular categories
Tau Stinger
Undergraduate Researcher
Mathematics Major (College of Arts & Sciences)
Anna Bedratenko
Undergraduate Researcher
Mathematics Major (College of Arts & Sciences)
Julia Plavnik
Faculty Mentor
Julia Plavnik (College of Arts & Sciences)
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 higher energy physics, condensed matter physics, and quantum computing. There are several notions of smallness for these categories. 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 some of the important numbers we use to measure the "size" of the category (such as the dimension and the rank). 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.