Caroline Mary Series (born 24 March 1951) is an English mathematician known for her work in

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P' ...

Kleinian group In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space . The latter, identifiable with , is the quotient group of the 2 by 2 complex matrices of determinant 1 by thei ...

s and

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

Early life and education

Series was born on 24 March 1951 in

Oxford Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the Un ...

to Annette and George Series. She attended Oxford High School for Girls and from 1969 studied at

Somerville College, Oxford Somerville College, a constituent college of the University of Oxford in England, was founded in 1879 as Somerville Hall, one of its first two women's colleges. Among its alumnae have been Margaret Thatcher, Indira Gandhi, Dorothy Hodgkin, Ir ...

, where she was interviewed for admission by Anne Cobbe. She obtained a B.A. in Mathematics in 1972 and was awarded the university Mathematical Prize. She was awarded a Kennedy Scholarship and studied at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

from 1972, obtaining her Ph.D. in 1976 supervised by George Mackey on the ''

Ergodicity In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies t ...

of product groups''.

Career and research

In 1976–77 she was a lecturer at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, and in 1977–78 she was a

research fellow A research fellow is an academic research position at a university or a similar research institution, usually for academic staff or faculty members. A research fellow may act either as an independent investigator or under the supervision of a p ...

Newnham College, Cambridge Newnham College is a women's constituent college of the University of Cambridge. The college was founded in 1871 by a group organising Lectures for Ladies, members of which included philosopher Henry Sidgwick and suffragist campaigner Millicent ...

. From 1978 she was at the

University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (202 ...

, first as a lecturer, then, from 1987, as a reader, and from 1992 as a professor. From 1999 to 2004 she was

Engineering and Physical Sciences Research Council The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to univers ...

(EPSRC) Senior Research Fellow at the University of Warwick. In the 1970s, Series found illustrations of Rufus Bowen's Theory of Dynamic Systems in the geometry of

continued fraction In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integ ...

s and two-dimensional hyperbolic geometry, effect of

Fuchsian group In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R). The group PSL(2,R) can be regarded equivalently as a group of isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations ...

s. After that she investigated similar, including fractal, geometric patterns in three-dimensional hyperbolic spaces, with

s as

symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the amb ...

s. The computer images led to a book project with

David Mumford David Bryant Mumford (born 11 June 1937) is an American mathematician known for his work in algebraic geometry and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded ...

and David Wright, which took over ten years. Other coauthors with whom she published in this area include Linda Keen and Joan Birman. Series became the third woman to be president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

when she held the post in 2017–2019. She is emeritus professor in mathematics at the University of Warwick.

Selected publications

* with

and David Wright: ''Indra's Pearls.'' Cambridge University Press 2002. * * *
Series, Wright ''Non euclidean geometry and Indra´s Pearls'', Plus Magazine
*

Awards and honours

In 1987 she was awarded the Junior

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehea ...

by the

. In 1992 she held the Rouse Ball Lecture in Cambridge, and in 1986 she was the

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Berkeley (''Symbolic Dynamics for Geodesic Flows''). From 1990 to 2001 she was the editor of the Student Texts of the London Mathematical Society. In 1986 she was a founding member of European Women in Mathematics (EWM). In 2009 she was the Emmy Noether visiting professor at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded i ...

. She was elected a

Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

in its inaugural class of 2013. She is an Honorary Fellow of Somerville College. *1972 –74 Kennedy Scholarship, Harvard University *1987 Junior Whitehead Prize, London Mathematical Society *2014

Senior Anne Bennett Prize The Anne Bennett Prize and Senior Anne Bennett Prize are awards given by the London Mathematical Society. In every third year, the society offers the Senior Anne Bennett prize to a mathematician normally based in the United Kingdom for work in, in ...

, London Mathematical Society *2016

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathematic ...

One or more of the preceding sentences incorporates text from the royalsociety.org website where: *2017 Elected to the

Academia Europaea The Academia Europaea is a pan-European Academy of Humanities, Letters, Law, and Sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europea ...

Personal life

She is the daughter of the physicist George Series.

References

{{DEFAULTSORT:Series, Caroline 1951 births Living people Alumni of Somerville College, Oxford Harvard University alumni 20th-century English mathematicians 21st-century English mathematicians British women mathematicians Academics of the University of Warwick Fellows of the American Mathematical Society Members of Academia Europaea Whitehead Prize winners Fellows of the Royal Society Female Fellows of the Royal Society Fellows of Somerville College, Oxford 20th-century women mathematicians 21st-century women mathematicians