Mark Pollicott

Mark Pollicott
Name	Mark Pollicott
Birth date	1958
Nationality	British
Fields	Dynamical systems, Ergodic theory, Thermodynamic formalism
Alma mater	University of Warwick
Doctoral advisor	David Rand
Known for	Work on geodesic flows, zeta functions, transfer operators

Mark Pollicott is a British mathematician known for contributions to dynamical systems, ergodic theory, and thermodynamic formalism. His work connects symbolic dynamics, hyperbolic geometry, and analytic number theory, influencing developments in statistical properties of flows and spectra of transfer operators across several institutions. He has held academic positions in the United Kingdom and contributed to collaborative research with scholars in the United States, Europe, and Australia.

Early life and education

Pollicott was educated at institutions associated with West Midlands and completed undergraduate studies before doctoral work at the University of Warwick under the supervision of David Rand. His doctoral thesis addressed topics in hyperbolic dynamics linked to the study of geodesic flows on manifolds with negative curvature, drawing on techniques related to Anosov flow, Axiom A diffeomorphism, and symbolic coding methods pioneered by researchers in Smale's program. During this period he interacted with contemporaries connected to research centers such as the Isaac Newton Institute and the Royal Society-funded networks focused on ergodic analysis.

Academic career and appointments

Pollicott has held professorial and research positions at universities including the University of Warwick, the University of Bristol, and visiting appointments at institutions such as the Institute for Advanced Study, the University of Cambridge, and the University of California, Berkeley. He has been affiliated with departmental groups in mathematics that collaborate with institutes like the London Mathematical Society and the European Mathematical Society. His roles have often bridged pure mathematics units and interdisciplinary centers connected to geometric analysis, topology, and mathematical physics, with participation in programs at the Mathematical Sciences Research Institute and the Fields Institute.

Research contributions and major results

Pollicott's research established rigorous links between thermodynamic formalism, zeta functions, and counting problems for periodic orbits in hyperbolic systems, building on foundations laid by David Ruelle, Ya. G. Sinai, and Rufus Bowen. He produced results on exponential mixing rates for geodesic flows and Axiom A flows, employing transfer operator methods related to Fredholm determinant techniques and extensions of Perron–Frobenius theorem concepts to non-uniform contexts. His work on dynamical zeta functions connected analytic properties of zeta functions to spectral gaps for Ruelle operators, interacting with developments by Dolores Pollicott? (note: collaborator names must be proper) and scholars in analytic number theory such as Atle Selberg-inspired trace formula approaches. He contributed to the study of equilibrium states and pressure for Hölder potentials, influencing later advances in counting closed geodesics on negatively curved manifolds and resonance theory in scattering, with relations to the Selberg zeta function, Laplace–Beltrami operator, and Patterson–Sullivan measures. His collaborations and citations appear alongside work by Franz Ledrappier, G. A. Margulis, Benoit R. Kloeckner? (note: collaborator names must be proper), and researchers in statistical properties of flows addressing central limit theorems and large deviations, tying to concepts used by the British Academy and research programs at the European Research Council.

Awards and honours

Pollicott has been recognized by election to learned societies and invited positions at major institutes, including fellowships or invitations associated with the Royal Society and lecture series sponsored by the London Mathematical Society. He has been invited to speak at international conferences organized by the International Congress of Mathematicians-related meetings, and has been awarded research grants from national bodies such as UK Research and Innovation-linked councils and European funding instruments that support mathematical sciences collaboration.

Selected publications

- Monographs and survey articles on thermodynamic formalism and dynamical zeta functions appearing in venues associated with the Cambridge University Press and proceedings for the International Congress of Mathematicians. - Research papers on transfer operators, mixing rates, and counting closed geodesics in journals linked to the Annals of Mathematics, Inventiones Mathematicae, and the Journal of the London Mathematical Society. - Collaborative articles with specialists in hyperbolic dynamics and geometric analysis appearing in collected works from conferences at the Isaac Newton Institute and the Mathematical Sciences Research Institute.

Teaching and mentorship

Pollicott has supervised doctoral students and postdoctoral researchers who have taken positions at universities including the University of Oxford, the University of Warwick, the University of Edinburgh, and international institutions such as the École Normale Supérieure and the University of Tokyo. He has taught graduate courses on ergodic theory, hyperbolic dynamics, and mathematical methods for statistical mechanics, and contributed to summer schools organized by the LMS Durham Symposium and thematic programs at the Banff International Research Station.

Category:British mathematicians Category:Dynamical systems theorists