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Explore advanced mathematical research on the relationship between periods of automorphic forms and special values of L-functions in this conference lecture from the Workshop on "Eisenstein Series, Spaces of Automorphic Forms, and Applications." Delve into groundbreaking joint work that formulates a global conjecture relating periods associated to symmetric spaces of unitary groups to central values of standard L-functions on linear groups, extending Waldspurger's theorem for GL(2) to more general cases. Discover the introduction of a new family of relative trace formulas constructed from the Bump-Friedberg integral and learn how these formulas are compared under specific local assumptions to prove instances of the proposed conjecture. Examine the novel aspect of relative endoscopy that emerges in this work, requiring the establishment of endoscopic comparisons of relative trace formulas to achieve global results. Understand how this theoretical framework builds upon several new local mathematical results that form the foundation for these advances in the relative Langlands program.
