Lie Groups Seminar

Speaker: Daniel Litt (University of Toronto) Title: Exceptional motives and exceptional local systems Abstract: In 1996, Serre asked about the existence of motives with exceptional motivic Galois group. Such motives are now known to exist for all exceptional groups, due to work of Gross–Savin, Katz, Dettweiler–Reiter, Yun, Patrikis, Boxer–Calegari–Emerton–Levin– Patrikis–Madapusi Pera, Guralnick–Lubeck–Yu, and Faegerman (and possibly others). For all exceptional groups except E6, families of such motives were known, but until recently this was open for E6. I’ll survey this story, explain joint work with Krämer–Maculan constructing families of exceptional E6-motives—arising from the classical geometry of cubic 3-folds—and speculate about similar constructions for other exceptional groups.