北京雁栖湖应用数学研究院

黄林哲 , 刘正伟 , 塞巴斯蒂安·帕尔库 , 王亦龙 , 吴劲松

Albert Ai

2022年08月24日 10:30 至 12:00

1110

Zoom 638 227 8222 (BIMSA)

Fusion categories have established themselves in the past two decades as indispensable objects of study across representation theory, low-dimensional topological quantum field theory, conformal field theory, and quantum computation. But this field of study is at a cross-roads since the production of high-level machinery and abstraction is far out-pacing the set of known examples. At the core of this crisis is the "categorification" problem of determining when there exists a fusion category realizing a given fusion ring, i.e. the combinatorial skeleton of a fusion category. The most elementary fusion rings are the integral character rings of finite groups; it is still a vast open problem to determine which fusion rings with exactly one noninvertible element have corresponding fusion categories. In this talk we will discuss the categorification problem for fusion rings whose basis elements take one of two dimensions. This is the setting where almost all known "exotic" examples of fusion categories live. At least the first half of the talk will be understandable by a general audience. ([2208.07319] Categorification of integral group rings extended by one dimension (arxiv.org)).

Albert Ai received his Bachelor's degree from Princeton University in 2013, and his PhD at the University of California, Berkeley in 2019, advised by Daniel Tataru. After holding a postdoctoral position at the University of Wisconsin-Madison, he is currently an assistant professor at BICMR. His research interests lie at the intersection of dispersive PDEs and harmonic analysis.