Time: June 19 (Tuesday) 10:00-11:00

Place: N212

Speaker: Terry Gannon (University of Alberta)

Title: Exceptional modular invariants are rare

Abstract: Let g be a simple finite-dimensional Lie algebra and k be a positive integer. An old question is to identify all possible modular invariants for g at level k. The result for g=sl(2) is the famous ADE classification of Cappelli-Itzykson-Zuber from 1987. Understanding this ADE pattern at a deeper level was a crucial original motivation for Ocneanu's work. Somewhat later, the analogous classification for g=sl(3) was found; that classification is intimately connected to Jacobians for Fermat curves. Little else is known. However, recent work makes the analogous classification for all Lie groups up to rank 8 or so imminent. The key step is a bound K(g) which grows like the cube of the rank of g: when the level k is greater than K(g), the only modular invariants come from symmetries of the extended Dynkin diagram of g. My talk will describe the problem and explain the bound.