The central scientific theme of this programme is the recent development of applications of ergodic theory to other areas of mathematics. In particular, the connections with geometry, group actions and rigidity, and number theory.
The potential of ergodic theory as a tool in number theory was revealed by Furstenberg's proof of Szemerdi's theorem on arithmetic progressions. Foremost amongst the recent contributions to number theory is the solution of the Oppenheim Conjecture, a problem on quadratic forms which had been open since 1929, and the Baker-Spindzuk conjectures in the metric theory of diophantine approximations.
Of equal importance is the role of ergodic theory in geometry and the rigidity of actions. The seminal result in this direction is the Mostow rigidity theorm. In recent years there have been diverse results, including rigidity results for higher rank abelian groups, and results on the classification of geodesic flows on manifolds of non-positive curvature.
This is a quickly evolving area of research. The program will explore these, and other, emerging applications of ergodic theory. It will bring together both national and international experts in ergodic theory and related disciplines, as well as others from the wider UK mathematical community.
Report: Download Report
On ergodic $\Bbb Z^d$ actions on Lie groups by automorphisms
Authors: SG Dani
Hyperbolic dynamical systems
Authors: Boris Hasselblatt
Cartan-decomposition subgroups of SU(2,n)
Authors: A Iozzi, Dave Witte
On automorophisms of arithmetic subgroups of unipotent groups in positive characteristic
Authors: Dave Witte, Lucy Lifschitz
Homogeneous Lorentz manifold with simple isometry group
Authors: Dave Witte
10 January 2000 to 14 January 2000
27 March 2000 to 31 March 2000
3 April 2000 to 7 April 2000
30 May 2000 to 30 May 2000
26 June 2000 to 30 June 2000
3 July 2000 to 7 July 2000
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The Isaac Newton Institute is a national and international visitor research institute. It runs research programmes on selected themes in mathematics and the mathematical sciences with applications over a wide range of science and technology. It attracts leading mathematical scientists from the UK and overseas to interact in research over an extended period.
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