| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | January 22, 2007 |
| Latest Amendment Date: | January 22, 2007 |
| Award Number: | 0714086 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Tie Luo
tluo@nsf.gov (703)292-8448 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 31, 2006 |
| End Date: | May 31, 2010 (Estimated) |
| Total Intended Award Amount: | $96,852.00 |
| Total Awarded Amount to Date: | $96,852.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
1608 4TH ST STE 201 BERKELEY CA US 94710-1749 (510)643-3891 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
1608 4TH ST STE 201 BERKELEY CA US 94710-1749 |
| 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: |
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| 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
The research project is focused on a broad range of questions concerning
algebraic stacks and their applications. The project is divided into two
parts. The first part concerns foundational problems which have arisen
in recent important applications of stacks such as the geometric
Langland's program, the theory of moduli of stable maps, and the
construction of moduli spaces for higher dimensional varieties. The
second part of the program concerns applications of the theory. In
particular new applications of the relationship between log geometry in
the sense of Fontaine and Illusie and stacks discovered by the PI in
earlier work, generalizations of the theory of twisted stable maps, as
well as applications to the construction and study of moduli spaces for
varieties of general type, abelian varieties, and vector bundles on
curves.
The notion of stack is a tool used to deal with internal symmetries of
mathematical objects, as well as actions of groups. For example, when
trying to classify geometric objects one is naturally forced to deal with
the symmetries of the objects in question. In recent years, the theory of
stacks has come to play an important role in almost every part of
algebraic geometry, arithmetic geometry, and mathematical physics and a
great number of exciting new applications of stacks have been found. This
is not surprising considering the importance of symmetries in mathematics
and other fields of science. This great interest in stacks has brought to
light a number of important problems about stacks. The research project
aims to broaden our understanding of both the foundational aspects of the
theory of stacks and as well as the many applications.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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