EPSRC Reference: 
EP/I003371/2 
Title: 
Stability conditions and hypermultiplet space 
Principal Investigator: 
Bridgeland, Professor T 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics and Statistics 
Organisation: 
University of Sheffield 
Scheme: 
Standard Research 
Starts: 
01 January 2014 
Ends: 
30 September 2014 
Value (£): 
113,157

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Many modern physical theories such as string theory are geometrical in nature,with the properties of particles and forces being determined by the way extradimensions in the theory are curled up on themselves. Unfortunately stringtheory is not at all wellunderstood at present, and it has not so far beenpossible to make predictions that can be experimentally verified. This projectfits into a large area of current research in pure mathematics which aims at abetter understanding the mathematcal structure of string theory. One could hopethat this will one day enable us to make calculations of real world quantitiesthat can then be checked against experiment. For now though it is early days,and our research focuses on properties of the curled up dimensions appearing instring theory, known in mathematics as CalabiYau manifolds.This particular proposal concerns certain algebraic objects appearing in string theorywhich physicists call categories of BPS branes, and mathematicians call CalabiYaucategories. We will be concerned with integers called DonaldsonThomas invariantswhich measure the precise number of BPS branes appearing in the theory. Theultimate aim is to better understand an object called the hypermultiplet space,an auxilliary space appearing in string theory but which has no mathematicaldefinition at present. The physics suggests that this space can be equipped witha geometrical structure which encodes the DonaldsonThomas invariants in aninteresting way. This geometrical structure is called a hyperkahler metric andexamples of such structures are of interest in both mathematics and theoretical physics.

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: 
http://www.shef.ac.uk 