Skeins on Tori

Skein theory is a basic notion in the field of quantum topology in which one studies knots and graphs in 3-dimensional spaces up to certain linear relations. I will describe some methods for studying skeins through the lens of algebra and representation theory. Some important notions from totally different areas of math appear in the study of skeins on tori, including Hecke algebras and q-difference equations. We will use these tools to extract explicit formulas for the dimensions of skein modules for the 3-torus. This is joint work with David Jordan, Monica Vazirani, and Haiping Yang. All are welcome and no prior knowledge of the subject will be assumed!