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Explore the cohomological interpretation of period integrals for automorphic representations through this 59-minute conference lecture from the Workshop on "Eisenstein Series, Spaces of Automorphic Forms, and Applications" at the Erwin Schrödinger International Institute. Discover how Archimedean modular symbols, defined as linear functionals on relative Lie algebra cohomology spaces, capture the Archimedean behavior of modular symbols and enable the definition of automorphic periods as an analogue to Deligne's periods for critical pure motives. Learn about the construction methodology that investigates the rationality of Archimedean modular symbols and examine how these tools, combined with rationality results for Eisenstein and cuspidal cohomology spaces, lead to significant findings about critical values of standard L-functions and Rankin-Selberg L-functions. Understand how these results support Blasius's conjecture and gain insights from recent collaborative research involving multiple mathematicians in the field of automorphic forms and L-functions.
