| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | April 1, 2024 |
| Latest Amendment Date: | April 1, 2024 |
| Award Number: | 2350049 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Jan Cameron
jcameron@nsf.gov (703)292-4544 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2024 |
| End Date: | June 30, 2027 (Estimated) |
| Total Intended Award Amount: | $145,055.00 |
| Total Awarded Amount to Date: | $47,255.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
9500 GILMAN DR LA JOLLA CA US 92093-0021 (858)534-4896 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
9500 GILMAN DRIVE LA JOLLA CA US 92093-0021 |
| 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): | ANALYSIS PROGRAM |
| Primary Program Source: |
01002526DB NSF RESEARCH & RELATED ACTIVIT 01002627DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): | |
| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The theory of von Neumann algebras, originating in the 1930's as a mathematical foundation for quantum physics, has since evolved into a beautifully rich subfield of modern functional analysis. Studying the precise structure of von Neumann algebras is rewarding for many reasons, as they appear naturally in diverse areas of modern mathematics such as dynamical systems, ergodic theory, analytic and geometric group theory, continuous model theory, topology, and knot theory. They also continue to be intimately involved in a variety of fields across science and engineering, including quantum physics, quantum computation, cryptography, and algorithmic complexity. The PI will focus on developing a new horizon for research on structural properties of von Neumann algebras, by combining entropy (quantitative) and boundary (qualitative) methods, with applications to various fundamental open questions. This project will also contribute to US workforce development through diversity initiatives and mentoring of graduate students and early career researchers.
In this project, the PI will develop two new research directions in the classification theory of finite von Neumann algebras: applications of Voiculescu's free entropy theory to the structure of free products and of ultrapowers of von Neumann algebras; the small at infinity compactification and structure of von Neumann algebras arising from relatively properly proximal groups. This will involve a delicate study of structure, rigidity and indecomposability properties via innovative interplays between three distinct successful approaches: Voiculescu's free entropy theory, Popa's deformation rigidity theory, Ozawa's theory of small at infinity boundaries and amenable actions.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Please report errors in award information by writing to: awardsearch@nsf.gov.
