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Please join us for pre-Colloquium Tea

This will be a nontechnical talk about our work with David Kazhdan on the spectrum of the Laplace and Hecke operators in the span of Eisenstein series. This very classical problem in the spectral theory of automorphic forms goes back to at least Langlands, who also introduced the analytic techniques that allow to find the spectrum in principle. To replace an in-principle answer by a concrete answer, we found it very useful to have a certain geometric interpretation of the multivariate contour integrals in Langlands’ setup. My goal in this talk will be to explain this geometric interpretation.

This is a 30min slow-pace pre-seminar discussion aiming to familiarise graduate students and postdocs with basic ideas used in Thursday Analysis Seminar talk. The focus will be put on ideas, and technicalities are kept to a minimum. 

Topics include: limiting absorption principle, scattering theory, manifolds with corners.