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Algebra and Combinatorics Seminar: Qing Zhang, Purdue, Classification of Modular Categories by Galois Orbit Count
November 9, 2022 | 12:45 pm - 1:45 pm EST
Given a modular category C, the irreducible characters of its fusion ring are in one-to-one correspondence with the set Irr(C) of isomorphism classes of simple objects of C. Consequently, the action of the absolute Galois group on these characters induces a permutation action on Irr(C). The analysis of this action is essential to the classification of modular categories, whether by rank or by other characteristics. Another essential property of a modular category is its associated (projective) SL(2,Z)-representation, whose kernel is a congruence subgroup. This gives another connection between the theory of modular categories and classical number theory.
I will talk about the recent progress on the classification of modular categories using representation and number theoretic methods. Then I will discuss the results regarding the classification of modular categories according to the number of Galois orbits. The talk is based on joint work with Siu-Hung Ng and Yilong Wang; and separate joint work with Julia Plavnik, Andrew Schopieray, and Zhiqiang Yu.
Speaker’s webpage: https://zhangqing2513.github.io/
Location: Jointly in person and virtually on Zoom. SAS 2225 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics mailing list, please contact Corey Jones at email@example.com to be added.