EPSRC Reference: 
EP/D071895/1 
Title: 
Quantum Frobenius manifolds, NelsonRegge algebra and RiemannHilbert problem. 
Principal Investigator: 
Mazzocco, Professor M 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Manchester, The 
Scheme: 
Advanced Fellowship 
Starts: 
01 October 2006 
Ends: 
30 September 2008 
Value (£): 
401,088

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Mathematical Analysis 
Mathematical Physics 
Nonlinear Systems Mathematics 

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 
Physical phenomena are generally described by differential equations. These are usually very difficult or impossible to solve. Nevertheless there is a special class of differential equations which are solvable in some sense. They are called integrable systems. When we manage to describe a physical phenomenon by an integrable system, we can understand and often predict its behavior. Recently the theory of integrable systems has been reformulated in the language of Frobenius manifolds. The theory of Frobenius manifolds lies at the crossroad of many disciplines in Pure, Applied Mathematics and Theoretical Physics. One of the beauties of this theory consists in its universality: results proved for a special class of Frobenius manifolds turn out to be true also for other classes of Frobenius manifolds. For example the isomorphy of certain Frobenius manifolds in quantum cohomology and in singularity theory is one version of mirror symmetry.In this project we plan to explore yet one more link between the theory of Frobenius manifolds and another fascinating branch of mathematics: the problem of quantization of Teichmuller space known in quantum gravity. This research will open up new lines of ground breaking research. In fact, it is always the case that when two rich branches of mathematics are unified, many interesting new question will arise and many unexpected result will be proved.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


Sectors submitted by the Researcher 
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Project URL: 
http://gow.epsrc.ac.uk/NGBOViewGrant.aspx?GrantRef=EP/D071895/1 
Further Information: 

Organisation Website: 
http://www.man.ac.uk 