Character sheaves on the loop Lie algebra and its global implications

Motivated by Lusztig’s definition of character sheaves on a reductive Lie algebra, we propose a definition of character sheaves on the loop Lie algebra. The construction can be viewed as a p-adic analogue of the orbit method, and the resulting sheaves are closely related to characters of supercuspidal representations of J.K.Yu. Further, the construction suggests a definition of wildly ramified Hitchin moduli spaces suitable for the study of ramified geometric Langlands. This is joint work with Bao Chau Ngo.