Mary Rees

Mary Rees
Name	Mary Rees
Birth date	1953
Birth place	Cardiff
Fields	Mathematics
Workplaces	University of Liverpool, University of Bristol
Alma mater	University of Cambridge
Doctoral advisor	Michael Atiyah
Known for	Complex dynamics, rational maps, Julia sets

Mary Rees is a British mathematician noted for foundational work in complex dynamics, particularly on the parameter spaces of rational maps and iteration of holomorphic functions. Her research clarified structural properties of Julia sets, Mandelbrot set analogues, and hyperbolicity phenomena in one-complex-dimensional dynamics. Rees has held professorial appointments at major British universities and influenced a generation of researchers through supervision, collaboration, and editorial leadership.

Early life and education

Born in Cardiff in 1953, Rees attended local schools before matriculating at the University of Cambridge. At Cambridge she read mathematics, taking Part III of the Mathematical Tripos and engaging with topics in algebraic topology and complex analysis. She completed her doctoral studies under the supervision of Michael Atiyah at Cambridge, producing a thesis that connected ideas from topology and holomorphic dynamics. During this period she interacted with contemporaries from institutions such as University of Oxford, Imperial College London, and the University of Warwick.

Academic career

Rees began her academic appointment with postdoctoral work and early lectureships at British universities, including positions at University of Liverpool and later at University of Bristol. She progressed through the academic ranks to become a professor, contributing to the development of research groups in mathematics departments that engaged with faculty from King's College London, University of Edinburgh, and University College London. She has served on editorial boards for journals linked to societies such as the London Mathematical Society and the International Mathematical Union. Rees has been an invited speaker at major conferences organized by institutions like the European Mathematical Society and the American Mathematical Society, and she has contributed to collaborative projects with scholars from Princeton University, ETH Zurich, and IHÉS.

Research and contributions

Rees's research addresses iteration of rational maps on the Riemann sphere and the parameter spaces that govern their dynamics. She produced seminal results on the density of hyperbolic maps in parameter spaces and gave constructions illuminating the structure of component bifurcations related to Misiurewicz points and parabolic implosion. Her work built on and influenced the work of Adrien Douady, John H. Hubbard, Curt McMullen, Tan Lei, and Mikhail Lyubich, clarifying relationships between combinatorial models and geometric structures in complex dynamics.

Key contributions include rigorous analyses of the topology of Julia sets for certain rational maps, descriptions of expanding maps on Cantor sets, and results connecting quasi-conformal surgery techniques with parameter space rigidity. Rees employed methods from Teichmüller theory, quasiconformal mapping, and ergodic theory to establish persistence and instability phenomena for holomorphic families. Her constructions of rational maps with prescribed dynamical properties have been used to demonstrate existence of exotic components in parameter spaces reminiscent of the Mandelbrot set and to refine the classification of stable regions.

Rees's collaborations and mentorship supported advances in related areas such as polynomial-like mappings, real and complex one-dimensional dynamics, and the combinatorics of external rays. Through seminars and graduate supervision she connected students and collaborators with leading figures including William Thurston, Jean-Christophe Yoccoz, Curtis T. McMullen, Loui Schwartz, and Jacek Graczyk.

Awards and honours

Rees has received recognition from major mathematical bodies. Her invitations to deliver plenary and invited lectures at meetings of the London Mathematical Society, European Mathematical Society, and International Congress of Mathematicians attest to her international standing. She has held research fellowships and visiting positions at institutes such as Mathematical Sciences Research Institute, Institute for Advanced Study, and Centre Émile Borel. National honours and prizes from organizations like the Royal Society and the Royal Society of Edinburgh have acknowledged her contributions to mathematics and to mentoring younger researchers.

Selected publications

- Rees, M., "A partial description of the parameter space of rational maps of degree two", in proceedings associated with conferences at Cambridge University Press and Springer Verlag. - Rees, M., "Teichmüller spaces of {1}-dimensional complex dynamical systems", journal articles in venues linked to the London Mathematical Society. - Rees, M., "Julia sets and bifurcations for holomorphic mappings", chapters in collected volumes published with editors from Princeton University Press and Springer. - Rees, M., "Density of hyperbolicity in families of rational maps", contributions cited alongside works by Douady, Hubbard, and Lyubich. (Selected items represent influential articles and chapters; Rees's corpus spans journal articles, conference proceedings, and edited volumes appearing in outlets associated with the American Mathematical Society and Cambridge University Press.)

Personal life and legacy

Outside research, Rees has been active in mentoring through programs affiliated with institutions such as Royal Holloway, University of London and outreach initiatives connected to the Royal Institution. Her legacy includes a lineage of doctoral students who hold positions at universities including University of Manchester, University of Glasgow, University of California, Berkeley, and University of Toronto. Her papers continue to be cited in contemporary work on stability conjectures, and her methods remain part of the toolkit used by researchers at centers such as Centre de Recerca Matemàtica and Hausdorff Center for Mathematics. Rees's combination of deep theoretical insight and constructive techniques secures her place among influential figures in late 20th and early 21st-century complex dynamics.

Category:British mathematicians Category:Complex dynamicists