Mark Pollicott

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Mark Pollicott (born September 24, 1959 in Nottingham ) is a British mathematician who deals with ergodic theory and dynamic systems with applications in geometry , analysis and number theory .

Pollicott graduated from the University of Warwick with a bachelor's degree in physics in 1981 and a master's degree in mathematics in 1982 and received his doctorate there in 1984 with William Parry (The Ruelle operator, zeta functions and the asymptotic distribution of closed orbits). From 1985 he was a lecturer at the University of Edinburgh , conducted research at the INIC in Porto from 1988 to 1992 and was a lecturer at the University of Warwick from 1992, where he became a reader in 1995 . From 1996 to 2005 he was Fielden Professor of Pure Mathematics at the University of Manchester (where he headed the Faculty of Pure Mathematics from 1997/98 and 2001 to 2004) and has been Professor in Warwick since 2005.

In 1983 he and Parry proved an analogue of the prime number theorem for closed orbits in hyperbolic flows. Proof of this came from Grigori Margulis (1969), but was not fully published and did not use dynamic zeta functions. In special cases he also proved theorems about the error term of the asymptotic distribution of the closed orbits in analogy to the Riemann Hypothesis.

He was visiting scholar at IHES (1984/85), Institute for Advanced Study (1987/88), Institut Fourier in Grenoble (1992), MSRI (1988), Isaac Newton Institute and 1990 visiting professor at Caltech . From 1992 to 1997 he had a Royal Society University Fellowship and in 1998/99 and 2007/8 he was a Royal Society Leverhulme Trust Fellow. In 2005 he received a Marie Curie Chair from the EU. In 2014 he was invited speaker at the ICM in Seoul (Zeta functions for Anosov flows).

From 1994 to 1997 and since 2005 he has been the editor of Ergodic Theory and Dynamical Systems.

In addition to being British, he has Portuguese citizenship.

Fonts

  • with Michiko Yuri: Dynamical Systems and Ergodic Theory, London Mathematical Society Student Text Series, Cambridge University Press 1998
  • Lectures on ergodic theory and Pesin theory on compact manifolds, Cambridge University Press 1993
  • with William Parry: Zeta functions and the periodic orbit structure of hyperbolic dynamics, Société Mathématique de France, Asterisque, Volume 187/188, 1990, pp. 1-268
  • with Parry: An analogue of the prime number theorem for closed orbits of Axiom A flows, Annals of Mathematics, Volume 118, 1983, pp. 573-591
  • On the rate of mixing of Axiom A flows, Inventiones Mathematicae, Volume 81, 1985, pp. 413-426
  • The differential zeta function for Axiom A attractors, Annals of Mathematics, Volume 131, 1990, pp. 331-354
  • Asymptotic distribution of closed geodesics, Israel J. Math., 52, 1985, 209-224
  • with Anatole Katok , G. Knieper, H. Weiss: Differentiability and analyticity of entropy for Anosov and geodesic flows, Inv. Math., 98, 1989, 581-597
  • with R. Sharp: Exponential error terms for growth functions on negatively curved surfaces, American J. Math., 120, 1998, 1019-1042
  • with R. Sharp: Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature, Inv. Math., 117, 1994, 275-302
  • Periodic orbits and Zeta functions, in Handbook of Dynamical Systems, Volume 1A, Elsevier 2002, pp. 409-452
  • Dynamical zeta functions and closed orbits for geodesic and hyperbolic flows, in Pierre Cartier u. a. (Ed.) Frontiers in Number Theory, Physics and Geometry , Volume 1, Springer Verlag 2006

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ^ Margulis Certain applications of ergodic theory to the investigation of manifolds of negative curvature , Funct. Analysis Applic., 3, 1969, 89-90
personal data
SURNAME Pollicott, Mark
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH September 24, 1959
PLACE OF BIRTH Nottingham