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Presented By: Student Number Theory Seminar - Department of Mathematics

Student Number Theory: Motivating endoscopy via an example with SL(2)

Ram Ekstrom

Endoscopy arises from the attempt to stabilize the trace formula. The "stabilization" of the trace formula is roughly speaking a procedure to make the trace formula more useful for applications and it is an extremely important tool in the Langlands program. I will attempt to motivate the role that endoscopy plays by gently walking through the stabilization of the elliptic regular part of the trace formula for SL(2). During our walkthrough, we will see glimpses of the (elliptic) endoscopic groups, transfer factors, endoscopic transfer of functions, cohomological invariants, etc.—objects which all occur naturally in the theory of endoscopy.

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