Mary Rees

Last updated

Susan Mary Rees, FRS (born 31 July 1953 [1] ) is a British mathematician and an emeritus professor of mathematics at the University of Liverpool since 2018, specialising in research in complex dynamical systems. [2] [3]

Contents

Career

Rees was born in Cambridge. After obtaining her BA in 1974 and MSc in 1975 at St Hugh's College, Oxford, she did research in mathematics under the direction of Bill Parry at the University of Warwick, obtaining a PhD in 1978. Her first postdoctoral position was at the Institute for Advanced Study from 1978 to 1979. Later she worked at Institut des hautes études scientifiques and the University of Minnesota. Following this she worked at the University of Liverpool until her retirement. She became professor of mathematics in 2002 and retired in 2018, becoming an emeritus professor.

She was awarded a Whitehead Prize of the London Mathematical Society in 1988. The citation [4] notes that, in particular,

Her most spectacular theorem [5] has been to show that in the space of rational maps of the Riemann sphere of degree d  2 those maps that are ergodic with respect to Lebesgue measure and leave invariant an absolutely continuous probability measure form a set of positive measure.

She also spoke at the ICM in 1990. [6] In recent years, much of Rees' work has focused on the dynamics of quadratic rational maps; i.e. rational maps of the Riemann sphere of degree two, including an extensive monograph. [7] In 2004, she also presented an alternative proof of the Ending Laminations Conjecture of Thurston, [8] which had been proved by Brock, Canary and Minsky shortly before. [9]

FRS

She was elected to a Fellowship of the Royal Society in 2002.

Family

Her father David Rees was also a distinguished mathematician, who worked on Enigma in Hut 6 at Bletchley Park. Her sister Sarah Rees is also a mathematician. [6]

Works

Related Research Articles

Conjecture Proposition in mathematics that is unproven

In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found. Some conjectures, such as the Riemann hypothesis or Fermat's Last Theorem, have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

Louis de Branges de Bourcia French American mathematician

Louis de Branges de Bourcia is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.

Oswald Teichmüller German mathematician

Paul Julius Oswald Teichmüller was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces. Teichmüller spaces are named after him. He was also a committed Nazi.

Curtis T. McMullen American mathematician

Curtis Tracy McMullen is an American mathematician who is the Cabot Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory.

In mathematics, the Teichmüller space of a (real) topological surface , is a space that parametrizes complex structures on up to the action of homeomorphisms that are isotopic to the identity homeomorphism. Teichmüller spaces are named after Oswald Teichmüller.

Dennis Sullivan American mathematician

Dennis Parnell Sullivan is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.

Bill Parry (mathematician) English mathematician

Professor William (Bill) Parry FRS was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.

Lipman "Lipa" Bers was a Latvian-American mathematician, born in Riga, who created the theory of pseudoanalytic functions and worked on Riemann surfaces and Kleinian groups. He was also known for his work in human rights activism.

James W. Cannon is an American mathematician working in the areas of low-dimensional topology and geometric group theory. He was an Orson Pratt Professor of Mathematics at Brigham Young University.

Inter-universal Teichmüller theory is the name given by mathematician Shinichi Mochizuki to a theory he developed in the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields equipped with an elliptic curve". The theory was made public in a series of four preprints posted in 2012 to his website. The most striking claimed application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture. Mochizuki and a few other mathematicians claim that the theory indeed yields such a proof but this has so far not been accepted by the mathematical community.

Caroline Series English mathematician

Caroline Mary Series is an English mathematician known for her work in hyperbolic geometry, Kleinian groups and dynamical systems.

Ricardo Mañé Ramirez was a Uruguayan mathematician, known for his contributions to dynamical systems and ergodic theory. He was a doctoral student of Jacob Palis at IMPA.

Yair Minsky

Yair Nathan Minsky is an Israeli-American mathematician whose research concerns three-dimensional topology, differential geometry, group theory and holomorphic dynamics. He is a professor at Yale University. He is known for having proved Thurston's ending lamination conjecture and as a student of curve complex geometry.

The Michael Brin Prize in Dynamical Systems, abbreviated as the Brin Prize, is awarded to mathematicians who have made outstanding advances in the field of dynamical systems and are within 14 years of their PhD. The prize is endowed by and named after Michael Brin, whose son Sergey Brin, is a co-founder of Google. Michael Brin is a retired mathematician at the University of Maryland and a specialist in dynamical systems.

Yael Dowker Israeli mathematician (1919–2016)

Yael Naim Dowker (1919–2016) was an English mathematician, prominent especially due to her work in the fields of measure theory, ergodic theory and topological dynamics.

Erica Gail Klarreich is an American mathematician, journalist and science popularizer.

Tan Lei Mathematician (1963-2016)

Tan Lei was a mathematician specialising in complex dynamics and functions of complex numbers. She is most well-known for her contributions to the study of the Mandelbrot set and Julia set.

Francis Bonahon French mathematician

Francis Bonahon is a French mathematician, specializing in low-dimensional topology.

Nikolai Georgievich Makarov is a Russian mathematician. He is known for his work in complex analysis and its applications to dynamical systems, probability theory and mathematical physics. He is currently the Richard Merkin Distinguished Professor of Mathematics at Caltech, where he has been teaching since 1991.

Jeffrey Brock American mathematician

Jeffrey Farlowe Brock is an American mathematician, working in low-dimensional geometry and topology. He is known for his contributions to the understanding of hyperbolic 3-manifolds and the geometry of Teichmüller spaces.

References

  1. GRO Register of Births: SEP 1953 4a 294 CAMBRIDGE – Susan M. Rees, mmn = Cushen
  2. Mary Rees profile Archived 23 January 2010 at the Wayback Machine , University of Liverpool
  3. "Dr. Mary Rees". University of Liverpool. 18 January 2008. Retrieved 2 January 2014.
  4. Bulletin of the London Mathematical Society 20 (1988), no. 6, p. 639.
  5. Positive measure sets of ergodic rational maps, Ann. Sci. École Norm. Sup. 19 (1986), no. 3, 383–407.
  6. 1 2 EWM. "Mary Reese". European Women in Mathematics. Archived from the original on 16 June 2018. Retrieved 25 February 2018.
  7. Views of parameter space: Topographer and resident, Asterisque 288 (2003)
  8. The Ending Laminations Theorem direct from Teichmüller geodesics, Preprint, 2004
  9. The classification of Kleinian surface groups, II: The Ending Lamination Conjecture, Preprint, 2004