#  Exceptional modular invariants are rare  

 



 **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.

 ![Terry Gannon gives a talk,titled `Exceptional modular invariants are rare'.](/sites/g/files/omnuum6611/files/mathpicture/files/img_5285_preview.jpeg)