| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | May 5, 2006 |
| Latest Amendment Date: | September 20, 2009 |
| Award Number: | 0604633 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Joanna Kania-Bartoszynska
jkaniaba@nsf.gov (703)292-4881 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2006 |
| End Date: | June 30, 2012 (Estimated) |
| Total Intended Award Amount: | $333,609.00 |
| Total Awarded Amount to Date: | $398,729.00 |
| Funds Obligated to Date: |
FY 2007 = $62,877.00 FY 2008 = $65,187.00 FY 2009 = $205,494.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
5801 S ELLIS AVE CHICAGO IL US 60637-5418 (773)702-8669 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
5801 S ELLIS AVE CHICAGO IL US 60637-5418 |
| 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): | TOPOLOGY |
| Primary Program Source: |
app-0107 01000809DB NSF RESEARCH & RELATED ACTIVIT 01000910DB NSF RESEARCH & RELATED ACTIVIT |
| 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
ABSTRACT FOR NSF PROPOSAL 0604633
There are three main components to this project. First,
Farb will continue to investigate mapping class groups and
the moduli space of Riemann surfaces. This topic lies at
the intersection of many areas of mathematics, from
algebraic geometry to low-dimensional topology to string
theory to geometric group theory. Farb will continue to
apply methods from discrete subgroups of Lie groups in
order to understand these objects, especially the "Torelli
group", which is a part of the oldest but least understood
part of the theory. Symmetry is a core idea in
mathematics. Farb will continue his work with S.
Weinberger on the broad program of classifying all spaces
(that is Riemannian manifolds) with symmetry. The ideas
used so far in this work have included the theories of
harmonic maps, large-scale geometry, and transformation
groups. In a third project, Farb will continue his work
with C. Hruska on bringing together techniques and ideas
from geometric group theory with those from discrete
subgroups of Lie groups in order to build the theory of
lattices in automorphism groups of 2-complexes. This is a
2-dimensional extension of Bass-Lubotzky's theory of tree
lattices, where wild new phenomena can occur. Throughout
each of the projects just described, Farb will continue to
work with and mentor many young students and researchers.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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