EPSRC Reference: 
EP/D071305/1 
Title: 
Mirror symmetry for flag varieties 
Principal Investigator: 
Rietsch, Professor K 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Kings College London 
Scheme: 
Advanced Fellowship 
Starts: 
01 September 2006 
Ends: 
29 August 2012 
Value (£): 
420,535

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Physics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
23 Mar 2006

Mathematics 2006 Fellowships Panel

Deferred

24 Apr 2006

Mathematics Fellowships Interview Panel

Deferred


Summary on Grant Application Form 
Algebra and geometry come together when studying the solution sets of polynomial equations in many variables  socalled algebraic varieties. My research centers on flag varieties, which are particularly beautiful algebraic varieties with a very rigid structure. For example they are 'homogeneous': They have a large (matrix) symmetry group which can translate any point into any other. Flag varieties come in series starting with the simplest example, the Riemann sphere, and reaching arbitrarily high dimension. Mirror symmetry came to the attention of mathematicians in the early 1990's when physicists made astounding and precise predictions about certain 3dimensional algebraic varieties and numbers of rational curves on them. Since then the process of unraveling what underlies these predictions has been progressing, and the field has become a major part of modern mathematics. In my research I propose to study mirror symmetry in the context of flag varieties. There has already been a great deal of work on the theory of quantum cohomology for flag varieties which arose out of mirror symmetry and is a very rich subject in its own right. But this research has been almost entirely from a classical perspective of quantum cohomology generalizing ordinary cohomology, which has not involved mirror symmetry at all. What has been left out is the mysterious mirror model, what the physicists used in their computations of numbers of rational curves, which holds the information about enumerative algebraic geometry in a completely different form. In my recent paper [14] I propose such a model explicitly for general flag varieties and relate it to quantum cohomology. The main goal of the proposed research is to use this mirror model to understand the deeper and more difficult GromovWitten theory for flag varieties.

Key Findings 
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk

Potential use in nonacademic 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: 
