## Event Date:

## Event Location:

- 6635 South Hall

The local Shimura correspondence relates representations of PGL_2

to those of the metaplectic cover of SL_2, where both groups are p-adic and

the representations are on C-vector spaces. Many pieces of the usual

construction break down, due to non-semisimplicity, when the

representations are instead taken over a field of positive characteristic.

The mod p case is especially problematic. In the specific case of the pair

(tilde{SL}_2, PGL_2), I will discuss an alternate approach, which involves

a comparison of certain Iwahori Hecke algebras of both groups, as well as

progress towards a classification of the mod p representations of the

metaplectic group.