Some results and techniques on the classification of certain weakly-integral modular categories (of small rank or small dimension)

PAUL BRUILLARD; CÉSAR GALINDO; SIU-HUNG NG; JULIA YAEL PLAVNIK; ERIC C. ROWELL; ZHENGHAN WANG

Snowbird

Otro; Mathematical Research Communities: Mathematics of Quantum Phases of Matter and Quantum Information (MRC); 2014

AMS

In this talk I will recall some definitions and techniques used in the classifications of modular categories. I will also spend some time giving some known results about the classification of (weakly-)integral modular categories of a fixed Frobenious-Perron dimension or small rank. Then I will give the classification of all modular categories of dimension 4m, where m is an odd square-free integer, and all rank 6 and rank 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7.