Fusion categories and number theory
演讲者
时间
2026年10月15日 12:15 至 13:00
地点
A4-1
摘要
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.
演讲者介绍
2010年，获得马赛数学研究所（I2M）博士学位；2014-2016年，在印度数学科学研究所（IMSc）做博士后研究；2019年，在清华大学丘成桐数学科学中心（YMSC）担任为期一年的访问学者；2020-2024年，在BIMSA助理研究员 ；2024年至今，在BIMSA副研究员 。
主要研究领域包括量子代数、量子对称性、子因子、平面代数和融合范畴。在《Advances in Mathematics》、《Quantum Topology》、《IMRN》等期刊发表过论文。
主要研究领域包括量子代数、量子对称性、子因子、平面代数和融合范畴。在《Advances in Mathematics》、《Quantum Topology》、《IMRN》等期刊发表过论文。