Beijing Institute of Mathematical Sciences and Applications

Linzhe Huang , Zhengwei Liu , Sebastien Palcoux , Yilong Wang , Jinsong Wu

Albert Ai

Wednesday, June 14, 2023 10:30 AM - 12:00 PM

A3-3-301

Zoom 559 700 6085 (BIMSA)

Understanding the symmetries of algebraic objects can help decrease their complexity by several fold, and this reduction in complexity is intensified when there are fewer and fewer fixed-points.  Typically one requires the unit or neutral element to be fixed by any symmetry, so a symmetry for which this is the only fixed-point has been called "fixed-point-free".  These are the most active of symmetries and have strong implications for the objects they act upon.  For example, a finite group with a fixed-point-free automorphism must be solvable; if the automorphism is order 2 then the group is abelian and the symmetry is inversion.   In this talk, we will attempt to generalize classical results on fixed-point-free automorphisms of finite groups to fusion rings and categories.  Of particular interest is understanding when/if combinatorial symmetries of fusion rings can be lifted to categorical symmetries of fusion categories.  This talk will be self-contained, aimed toward a general audience, and will include copious amounts of examples.

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.