The local Langlands correspondence and character sheaves

David Roe

The local Langlands correspondence is a theorem for GL(n) due to Harris, Taylor and Henniart, and recent work of Arthur makes good progress toward establishing it for all classical groups. In this talk I will describe a different approach to local Langlands, pioneered by DeBacker and Reeder, that works for arbitrary split reductive groups but imposes restrictions on the starting Galois representation.

In particular I will focus on two stories: the extension of their method to tamely ramified unitary groups, and the beginnings of an effort to geometrize the method using character sheaves (joint with Clifton Cunningham).