Mathematical Sciences: Algebra, Number Theory and Algebraic Geometry
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
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This research will continue the research of the Principal                  Investigators' in number theory and representation theory.                      Kazhdan's projects include the study of affine flag manifolds,                  the trace formula and the cuspidal geometry of reductive groups                 over local fields.  Gross is studying certain Heegner cycles on                 Shimura varieties associated to orthogonal groups as well as                    generalizations of the class-number formula.  Tate is working on                height pairings for abelian varieties, refinements of the                       conjecture of Birch and Swinnerton-Dyer as well as the                          classification of certain 3-dimensional regular algebras.                            All three of these researchers work on the bridge area that                applies algebraic and geometric techniques to answer questions in               number theory.  Ultimately the goal is to solve equations in                    integers.  The geometric objects these equations define are the                 main objects of study.
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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