Ergodic Theory and Analysis

The Ergodic Theory and Analysis group at Manchester currently has 5 members, whose combined research interests cover a wide range of topics. We organize an Ergodic Theory network funded by the London Mathematical Society, which supports a series of one-day meetings in Manchester, Bristol, Liverpool, Queen Mary, Surrey and Warwick.

Research Interests

Broadly speaking, analysis is the study of functions, operators and measures and spaces associated to them. The latter are often infinite dimensional vector spaces (e.g. Banach spaces, Hilbert spaces) and may have additional structure (e.g. C*-algebras). Ergodic theory is the study of dynamical systems in the presence of a measure. A wide variety of analytic techniques are used, including the spectral properties of families of operators and the analysis of dynamical zeta functions. Zeta functions also arise in the applications of analysis to number theory and many dynamical systems have their origins in arithmetic. Noncommutative geometry seeks to understand spaces as if they were algebras of operators.

Members of Staff interests

Dr Mark Coleman: Analytic number theory; distribution of Gaussian primes; sieve methods; arithmetic functions.

Professor Roger Plymen (Emeritus): Noncommutative geometry; C*-algebras attached to p-adic groups; the relation between K-theory, group representations and algebraic number theory; the local Langlands correspondence; Skewes' number.

Professor Richard Sharp: Ergodic theory of hyperbolic systems; distribution of periodic orbits; dynamical zeta functions; applications to geometry and quantum chaos; links between noncommutative geometry and hyperbolic dynamical systems.

Dr Nikita Sidorov: Arithmetic dynamics; beta-expansions; Pisot and Salem numbers; Bernoulli convolutions; joint spectral radii.

Dr Charles Walkden: Ergodic theory of hyperbolic dynamical systems. Thermodynamic formalism. Probabilistic, dimension-theoretic, and rigidity properties of skew-product dynamics.

Members of staff involved: