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BIMSA-Tsinghua Quantum Symmetry Seminar
Categorical Fermionic Actions and Minimal Modular Extensions
Categorical Fermionic Actions and Minimal Modular Extensions
Organizers
Speaker
César Galindo
Time
Wednesday, July 9, 2025 10:30 AM - 12:00 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
This talk explores the theory of minimal modular extensions of braided fusion categories, with a particular focus on the non-Tannakian (super-Tannakian) case. After reviewing the notion of minimal modular extensions as introduced by Müger, I will present an obstruction theory that determines when such extensions exist. In the Tannakian case, we describe a concrete obstruction in $H_4(G,\mathbb{C}^*)$; for the super-Tannakian setting, we develop a complete cohomological obstruction theory.
A central theme of the talk is the introduction of categorical fermionic actions, which generalize group actions to the context of super-groups acting on fermionic fusion categories. This framework enables the classification of minimal modular extensions in the super-Tannakian setting and reveals new phenomena absent from the classical case.
These results complement recent work by Johnson-Freyd and Reutter on slightly degenerate categories and contribute to the broader program of classifying modular categories via their minimal extensions.
This is based on joint work with César Venegas-Ramírez.
A central theme of the talk is the introduction of categorical fermionic actions, which generalize group actions to the context of super-groups acting on fermionic fusion categories. This framework enables the classification of minimal modular extensions in the super-Tannakian setting and reveals new phenomena absent from the classical case.
These results complement recent work by Johnson-Freyd and Reutter on slightly degenerate categories and contribute to the broader program of classifying modular categories via their minimal extensions.
This is based on joint work with César Venegas-Ramírez.
Speaker Intro
César Galindo is a professor of mathematics at Universidad de los Andes, Bogotá, Colombia. His research interests focus on the representation theory of quantum groups and fusion categories, with an emphasis on applications to quantum computing.