EPSRC Reference: 
GR/T19117/01 
Title: 
Pair correlations of length spectra, quantum chaos and thermodynamic formalism 
Principal Investigator: 
Pollicott, Professor M 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Warwick 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 March 2005 
Ends: 
29 February 2008 
Value (£): 
139,180

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Mathematical Physics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
One of the most exciting interdisciplinary fields to emerge in recent years is at the intersection of three of the most important and active research areas in Mathematics: Number Theory, Geometry and Mathematical Physics. One goal in this theory, Quantum Chaos, is to understand from a geometric vantage point certain natural analytically defined characteristics (eigenvalues of the Laplacian) associated to manifolds. A very fruitful approach is to study the intimately related set of values given by the lengths of closed geodesics. In particular, by interpreting these as closed orbits of an associated dynamical system (the geodesic flow) we can bring to bear many powerful tools from ergodic theory and the general theory of dynamical systems. More precisely, important aspects of the spectral theory and Quantum Chaos, such as pair correlation's and the determinant of the Laplacian are amenable to study using symbolic dynamics and Thermodynamic Formalism.

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Further Information: 

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