Frontiers in Number Theory, Physics, and Geometry II
The present book collects most of the courses and seminars delivered at the meetingentitled“FrontiersinNumberTheory,PhysicsandGeometry”,which tookplaceattheCentredePhysiquedesHouchesintheFrenchAlps,March9- 21,2003.Itisdividedintotwovolumes.VolumeIcontainsthecontributionson three broad topics: Random matrices, Zeta functions and Dynamical systems. Thepresentvolumecontainssixteencontributionsonthreethemes:Conformal ?eld theories for strings and branes, Discrete groups and automorphic forms and ?nally, Hopf algebras and renormalization. The relation between Mathematics and Physics has a long history. Let us mentiononlyordinarydi?erentialequationsandmechanics,partialdi?erential equations in solid and ?uid mechanics or electrodynamics, group theory is essential in crystallography, elasticity or quantum mechanics. The role of number theory and of more abstract parts of mathematics such as topological, di?erential and algebraic geometry in physics has become prominent more recently. Diverse instances of this trend appear in the works of such scientists as V. Arnold, M. Atiyah, M. Berry, F. Dyson, L. Faddeev, D. Hejhal, C. Itzykson, V. Kac, Y. Manin, J. Moser, W. Nahm, A. Polyakov, D. Ruelle, A. Selberg, C. Siegel, S. Smale, E. Witten and many others. In 1989 a ?rst meeting took place at the Centre de Physique des Houches. The triggering idea was due at that time to the late Claude Itzykson (1938- 1995). The meeting gathered physicists and mathematicians, and was the occasion of long and passionate discussions.
very distinguished international list of authors including Alain Connes, a Fields Medallist.Cutting-edge research in well-written expository form