| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | May 20, 2008 |
| Latest Amendment Date: | May 20, 2008 |
| Award Number: | 0805833 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Christopher Stark
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | June 1, 2008 |
| End Date: | May 31, 2012 (Estimated) |
| Total Intended Award Amount: | $128,000.00 |
| Total Awarded Amount to Date: | $128,000.00 |
| Funds Obligated to Date: |
|
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
2221 UNIVERSITY AVE SE STE 100 MINNEAPOLIS MN US 55414-3074 (612)624-5599 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
2221 UNIVERSITY AVE SE STE 100 MINNEAPOLIS MN US 55414-3074 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | TOPOLOGY |
| Primary Program Source: |
|
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Abstract
Award: DMS-0805833
Principal Investigator: Tyler D. Lawson
The goal of this project is to relate the theory of formal group
laws to phenomena in stable homotopy theory and K-theory. In
stable homotopy theory, the objective is to begin making
fundamental computations in the theory of topological automorphic
forms developed in joint work with Behrens. This will first
proceed by examining and computing the homotopy of spectra
associated to certain moduli of abelian surfaces such as Shimura
curves, and then by working towards higher chromatic filtrations.
In algebraic K-theory, the objective is to make systematic use of
the relationship between formal group laws and complex cobordism
to systematize computations in algebraic K-theory and relate them
to the chromatic filtration, with the hope of gaining
understanding of the "chromatic redshift" phenomenon.
The subject of homotopy theory arose as a method to answer
concrete questions in geometry by way of algebra. In the
process, a strange connection was discovered with formal group
laws, which themselves are intimately related to quite different
subjects such as number theory and elliptic curves. In
particular, there is a surprising connection between elliptic
curves and mathematical physics. This research focuses on
applying very recent developments in homotopy theory to study
connections such as these, with the hope that our understanding
of number theory and our understanding of homotopy theory can
benefit each other.
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.
