Categorification of Integral Group Rings Extended by One Dimension

Explore a research seminar that delves into the categorification problem of fusion rings and their relationship to fusion categories, focusing specifically on those with basis elements of two dimensions. Learn about the current challenges in fusion category theory, where theoretical machinery has outpaced known examples, particularly in determining which fusion rings with exactly one noninvertible element correspond to fusion categories. Discover how integral character rings of finite groups serve as elementary fusion rings and examine the setting where most known "exotic" examples of fusion categories exist. Gain insights from speaker Andrew Schopieray, a mathematician whose journey from professional cooking to tensor category theory demonstrates an unconventional path in academic mathematics. Access supplementary materials including slides and related research papers to deepen understanding of this complex mathematical topic that spans representation theory, topological quantum field theory, conformal field theory, and quantum computation.