| EPSRC Reference: |
GR/T00924/01 |
| Title: |
Derived Equivalence, Braid Relations and Stability Conditions |
| Principal Investigator: |
Chuang, Professor J |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
03 October 2005 |
Ends: |
02 October 2007 |
Value (£): |
90,327
|
| EPSRC Research Topic Classifications: |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
|
Representation theory is the mathematical study of symmetry and of the various ways symmetry manifests itself in nature. A wonderful blend of algebra, geometry, and combinatorics, it enjoys fruitful interactions with physics and chemistry.The proposed research introduces a completely new approach to some fundamental unsolved problems in representation theory, based on modem methods of derived equivalences developed in the recent proof of Broue's conjecture for symmetric groups. This approach applies in particular to Lusztig's famous and influential conjecture on characters of irreducible modules for general linear groups in prime characterisctic, which has inspired major advances in mathematics even outside representation theory proper and continues to be a subject of intense study.The first part of research concerns extensions and applications of the derived equivalence methods in several directions and aims to culminate in a uniform proof of the existence of braid group actions on derived categories. These actions should provide a foundation around which to build a deeper understanding of a whole family of representation theories. The second part of research tackles the famous numerical conjectures of Lusztig and James by investigating certain small wreath products using the braid relations appearing in the first part together with an exciting new idea coming from mathematical physics, the stability conditions of Bridgeland and Douglas.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.bris.ac.uk |