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# Xinwen Zhu (Caltech), Geometric Methods in Representation Theory Seminar

## September 15, 2017 @ 4:30 pm - 5:30 pm

**Title: ***Spectral operators as a trace*

**Abstract: **I will first give a new formalism of (some parts of) the Springer theory and Deligne-Lusztig theory. Then I will use the new formalism to study the affine case, and construct the spectral operators acting on the local Hitchin moduli and the moduli of local Shtukas. In the former case, the construction generalizes the action of the affine Weyl group on the cohomology of affine Springer fibers constructed by Lusztig. In the latter case, the construction generalizes V. Lafforgue’s S-operators.