| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | April 27, 2007 |
| Latest Amendment Date: | March 25, 2009 |
| Award Number: | 0706784 |
| 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: | July 1, 2007 |
| End Date: | June 30, 2011 (Estimated) |
| Total Intended Award Amount: | $219,938.00 |
| Total Awarded Amount to Date: | $219,938.00 |
| Funds Obligated to Date: |
FY 2008 = $66,757.00 FY 2009 = $60,743.00 |
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
438 WHITNEY RD EXTENSION UNIT 1133 STORRS CT US 06269-9018 (860)486-3622 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
438 WHITNEY RD EXTENSION UNIT 1133 STORRS CT US 06269-9018 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | PROBABILITY |
| Primary Program Source: |
01000809DB NSF RESEARCH & RELATED ACTIVIT 01000910DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
This project is devoted to the study of stochastic analysis in
infinite dimensions. The main topic is stochastic differential
equations (SDEs) in infinite-dimensional spaces, such as
infinite-dimensional groups, loop groups and path spaces,
non-commutative $L^p$-spaces. The questions of existence and
uniqueness of solutions of the SDEs and smoothness of solutions will
be studied. These solutions will be used to construct and study heat
kernel measures (a non-commutative analogue of Gaussian or Wiener
measure) on infinite-dimensional manifolds such as an
infinite-dimensional Heisenberg group and the Virasoro group. In
general these infinite-dimensional spaces do not have an analogue of
the Lebesgue measure or a Haar measure in the group case. The PI
intends to study Cameron-Martin type quasi-invariance of these
measures. It is an interesting question in itself, and in addition it
can give rise to unitary representations of the infinite-dimensional
groups. It is proposed to study properties of square-integrable
holomorphic functions, including non-linear analogues of the
Segal-Bargmann transform and bosonic Fock space representations.
The intellectual merit of this proposal is in providing a better
understanding of Gaussian-type measures on infinite-dimensional
curved spaces. In particular, the proposed research will connect
diverse fields: stochastic analysis, geometric analysis and
mathematical physics. This research project has broader impacts on
diverse areas of mathematics, and it involves activities which help
to disseminate the knowledge of new findings in the field. The
proposed research is motivated by several subjects.
Infinite-dimensional spaces such as loop groups and path spaces
appear in physics, for example, in quantum field theory and string
theory. The PI proposes to formalize and study some of the notions
used in physics, such as measures on certain infinite-dimensional
spaces. In addition, it has a significant educational component,
namely, it involves two graduate students of the PI.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
Please report errors in award information by writing to: awardsearch@nsf.gov.
