Tame supercuspidals at bad primes Tame supercuspidals at bad primes

Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups and arise in number theory as local factors of cuspidal automorphic representations. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem. Although the problem has been solved for large p, a solution remains out of reach in general. I'll discuss work in progress joint with Jessica Fintzen towards constructing some of the missing "tamely ramified" supercuspidals when p is (very!) small.