Fusion categories and number theory
Organizers
Speaker
Time
Thursday, October 15, 2026 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
This talk explores connections between fusion categories and number theory:
- Starting from elementary examples of fusion rings, we explain how cyclotomicity, Galois symmetry and divisibility constrain categorification.
- An infinite Fibonacci family of rank-four simple integral fusion rings illustrates a Diophantine construction.
We then briefly discuss:
- the relations among modular fusion categories, the modular group and modular forms;
- how generalizing the length-finiteness of Egyptian fractions summing to 1 leads to rank-finiteness for modular fusion categories;
- how Stark's conjectures link the unitarity of cyclic near-group fusion categories to Hilbert's twelfth problem.
- Starting from elementary examples of fusion rings, we explain how cyclotomicity, Galois symmetry and divisibility constrain categorification.
- An infinite Fibonacci family of rank-four simple integral fusion rings illustrates a Diophantine construction.
We then briefly discuss:
- the relations among modular fusion categories, the modular group and modular forms;
- how generalizing the length-finiteness of Egyptian fractions summing to 1 leads to rank-finiteness for modular fusion categories;
- how Stark's conjectures link the unitarity of cyclic near-group fusion categories to Hilbert's twelfth problem.
Speaker Intro
2010, obtained a doctorate from Institut de Mathématiques de Marseille (I2M); 2014-2016, Postdoc in Institute of Mathematical Sciences (IMSc); 2019, One-year visitor at Yau Mathematical Sciences Center (YMSC), Tsinghua University; 2020-2024, Assistant Professor at BIMSA; 2024-now, Associate Professor at BIMSA.
Main Research Fields include Quantum Algebra, Quantum Symmetry, Subfactor, Planar Algebra and Fusion Category.
Published papers in the journals Advances in Mathematics, Quantum Topology, IMRN, etc...
Main Research Fields include Quantum Algebra, Quantum Symmetry, Subfactor, Planar Algebra and Fusion Category.
Published papers in the journals Advances in Mathematics, Quantum Topology, IMRN, etc...