Department of Mathematics - Seminar on Pure Mathematics - Mining for modular data from congruence representations

Modular fusion categories (MFCs) arise naturally in many areas of mathematics and physics. Associated with an MFC is a pair of complex matrices, called modular data, which are arguably the most important invariants of an MFC. The modular data of an MFC generate some uncanonical congruence representations of SL(2,Z). In this talk, we will discuss how modular data could be reconstructed or discovered from congruence representations of SL(2,Z). The talk is based on a joint work with Eric Rowell, Zhenghan Wang and Xiao-Gang Wen.