| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | March 21, 2003 |
| Latest Amendment Date: | August 30, 2007 |
| Award Number: | 0245606 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Tomek Bartoszynski
tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | April 1, 2003 |
| End Date: | February 29, 2008 (Estimated) |
| Total Intended Award Amount: | $0.00 |
| Total Awarded Amount to Date: | $110,659.00 |
| Funds Obligated to Date: |
FY 2004 = $23,389.00 FY 2005 = $0.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
77 MASSACHUSETTS AVE CAMBRIDGE MA US 02139-4301 (617)253-1000 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
77 MASSACHUSETTS AVE CAMBRIDGE MA US 02139-4301 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ALGEBRA,NUMBER THEORY,AND COM |
| Primary Program Source: |
app-0104 app-0105 |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
DMS-0245606
Vogan, David A.
Abstract
Title: Arthur's Conjecture, Spectural Theory, and Analytic Number Theory in Higher Rank
Abstract.
The proposal concerns two problems with applications to
automorphic forms. The first problem is in representation theory:
it is a conjecture in local harmonic analysis that is
motivated by taking Arthur's conjectures together with results
of Burger, Li and Sarnak. This problem is of interest as a
question in representation theory; it also offers a testing
ground for Arthur's conjectures and affords the possibility
of a better understanding of the automorphic spectrum. The
second problem is to study analytic number theory in the context
of automorphic forms on groups of higher rank. The dream goal of
this is a better understanding of higher moments of L-functions,
but there are a number of easier and concrete problems, such as
the development of large-sieve inequalities, whose solution would
also have immediate consequences for analytic number theory.
The project concerns two questions in the field of
``automorphic forms.'' This is a relatively new field of mathematics,
guided by the Langlands program -- it seeks to establish
connections between certain (apparently) far-separated
areas of mathematics. These connections have allowed work in
automorphic forms to have a significant impact in other fields.
Many cryptographic algorithms -- necessary for secure communication
over the Internet -- are based on
very subtle properties of prime numbers, and underlying
many of these algorithms are difficult results from analytic number
theory and automorphic forms. Another application
of automorphic forms has been the construction of ``Ramanujan graphs''
-- these are graphs with remarkable connectivity, and have had
application to communication networks and to theoretical computer
science. The questions under consideration will deepen
our understanding of automorphic forms. In addition
to the type of application just discussed,
these questions lie at the intersection of different fields of
mathematics, and will encourage collaboration between experts
in these different fields.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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