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Stacks in Representation Theory, Relative Trace Formula and analysis of Automorphic Periods (STACKSRTFPERIODS)
Start date: Mar 1, 2012, End date: Aug 31, 2017 PROJECT  FINISHED 

"One of the central problems in number theory is to prove somereasonably sharp bounds for values of $L$-functions and ofcorresponding automorphic periods (they are usually called ""subconvexitybounds""). In this project I propose to study two new toolsin representation theory of reductive groups over local fields-- Densities on Stcks and Mirolocalization of representtions.I am going to use these tools to obtain very strong subconvexity boundsfor periods of automorphic representations. This is an extensionof my recent work with A. Reznikov where we established thesebounds in some special case.These tools will also have many other applications to problemsin Representation theory and the theory of automorphic forms(e.g. Langlands' functoriality conjecture)."

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