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Historically, Langlands has introduced the theory of endoscopy in order to measure the failure of automorphic forms from being distinguished by their L-functions as well as the defect of stability in the Arthur-Selberg trace formula and `-adic cohomology of Shimura varieties. However, the number of important achievements in the domain of automorphic forms(More)
Recently, a new approach to functoriality of automorphic representations [L1] has been proposed in [FLN] following earlier work [L2, L3, L4] by Robert Langlands. The idea may be roughly summarized as follows. Let G and H be two reductive algebraic groups over a global field F (which is either a number field or a function field; that is, the field of(More)
Ngô Bao Châu has been awarded a Fields Medal for his proof of the fundamental lemma. I shall try to describe the role of the fundamental lemma in the theory of automorphic forms. I hope that this will make it clear why the result will be a cornerstone of the subject. I will also try to give some sense of Ngô’s proof. It is a profound and beautiful argument,(More)
MR2653248 (2011h:22011) 22E35; 11S37, 14D23, 14G35, 22E50 Ngo, Bao Chau Le lemme fondamental pour les algebres de Lie. Publications Mathematiques. Institut de Hautes Etudes Scientifiques (2010), no. 111, 1–169. The present paper, for which its author was awarded a Fields Medal, had achieved, even before publication, considerable fame and the Proceedings of(More)
The Australian Zebra Finch, Taeniopygia guttata, is a common vertebrate model for understanding behavioral, neurological, and physiological changes across the life span. The goal of this study was to determine if color in the environment can act as a stimulus and activate the zebra finch stress response. Zebra finches are diurnal and have color vision.(More)
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