Character sheaves for complex groups                  
-- David Nadler, December 11, 2009                                                             
                                  
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For every complex reductive group G, one can define a
(partial) 3d topological field theory (TFT)               
that assigns Lusztig's character sheaves to the circle. This
TFT encodes the Hecke algebra of the group                  
as well as the representation theory of its real forms. I will
survey its construction and structure; this is             
joint work (arXiv:0904.1247) with D. Ben-Zvi (Texas).