Quantum Fourier analysis
MATHEMATICAL PICTURE LANGUAGE
Zhengwei Liu - Tsinghua University
Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory and topological quantum field theory) with analytic estimates. We give an overview of quantum Fourier analysis in this talk. We highlight an application in recent work joint with Sebastien Palcoux and Jinsong Wu: we find new, surprisingly efficient, analytic obstructions of unitary categorification of fusion rings by applying quantum Fourier analysis to the Drinfeld center of unitary fusion categories.