"One of the central problems in number theory is to prove some
reasonably sharp bounds for values of $L$-functions and of
corresponding automorphic periods (they are usually called ""subconvexity
bounds""). In this project I propose to study two new tools
in 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 bounds
for periods of automorphic representations. This is an extension
of my recent work with A. Reznikov where we established these
bounds in some special case.
These tools will also have many other applications to problems
in Representation theory and the theory of automorphic forms
(e.g. Langlands' functoriality conjecture)."
Call for proposal
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