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Tom Willmore | |
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Willmore in 1979 at the Mathematical Research Institute of Oberwolfach, photo by Prof. Konrad Jacobs. | |

Born | Gillingham, England | 16 April 1919

Died | 20 February 2005 85) | (aged

Residence | |

Nationality | |

Alma mater | King's College London |

Known for | Willmore energy, Willmore flow, Willmore conjecture |

Scientific career | |

Fields | Mathematician |

Institutions | King's College London, University of Durham, University of Liverpool |

Notes | |

Note: PhD written/gained during WWII, advisor unknown |

**Thomas James Willmore** (16 April 1919 – 20 February 2005) was an English geometer. He is best known for his work on Riemannian 3-space and harmonic spaces.

The **English people** are a nation and an ethnic group native to England who speak the English language. The English identity is of early medieval origin, when they were known in Old English as the *Angelcynn*. Their ethnonym is derived from the Angles, one of the Germanic peoples who migrated to Great Britain around the 5th century AD. England is one of the countries of the United Kingdom, and the majority of people living there are British citizens.

**Riemannian geometry** is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a *Riemannian metric*, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.

Willmore studied at King's College London. After his graduation in 1939, he was appointed as a lecturer, but the onset of World War II led him to working as a scientific officer at RAF Cardington, working mainly on barrage balloon defences. During the war, he found the time to write his Ph.D. on relativistic cosmology, and gained his Ph.D. on *Clock regraduations and general relativity* as an external student of the University of London in 1943 .

In 1946, he was given a lectureship at the University of Durham. He wrote an influential book with Arthur Geoffrey Walker and HS Ruse entitled *Harmonic Spaces* in 1953. He left Durham in 1954 for the University of Liverpool to join Walker, after a supposed dispute between Willmore and a Durham colleague who refused to order German textbooks after being wounded in World War I.

**Durham University** is a collegiate public research university in Durham, North East England, founded by an Act of Parliament in 1832 and incorporated by Royal Charter in 1837. It was one of the first universities to commence tuition in England for more than 600 years, after Oxford and Cambridge, and is one of the institutions to be described as the third-oldest university in England. As a collegiate university its main functions are divided between the academic departments of the university and its 16 colleges. In general, the departments perform research and provide teaching to students, while the colleges are responsible for their domestic arrangements and welfare.

**Arthur Geoffrey Walker** was a leading mathematician who made important contributions to physics and physical cosmology. Although he was an accomplished geometer, he is best remembered today for two important contributions to general relativity. Together with H. P. Robertson, the well-known Robertson–Walker metric for the Friedmann–Lemaître–Robertson–Walker cosmological models, which are exact solutions of the Einstein field equation. Together with Enrico Fermi, he introduced the notion of Fermi–Walker differentiation.

The **University of Liverpool** is a public university based in the city of Liverpool, England. Founded as a college in 1881, it gained its royal charter in 1903 with the ability to award degrees and is also known to be one of the six original 'red brick' civic universities. It comprises three faculties organised into 35 departments and schools. It is a founding member of the Russell Group, the N8 Group for research collaboration and the university management school is AACSB accredited.

In 1965, Willmore returned to Durham, where he was appointed Professor of Pure Mathematics. He was elected Vice President of the London Mathematical Society in 1977, a post he held for two years. During that time, he was elected a member of The Royal Academies for Science and the Arts of Belgium.

**The London Mathematical Society** (**LMS**) is one of the United Kingdom's learned societies for mathematics.

Willmore retired from the University of Durham in 1984 after holding the position of Head of the Department of Mathematical Sciences on three separate occasions, covering most of his Professorship there. He was given an honorary degree from the Open University in 1994.

An **honorary degree** is an academic degree for which a university has waived the usual requirements, such as matriculation, residence, a dissertation, and the passing of comprehensive examinations. It is also known by the Latin phrases *honoris causa* or *ad honorem* . The degree is typically a doctorate or, less commonly, a master's degree, and may be awarded to someone who has no prior connection with the academic institution or no previous postsecondary education. An example of identifying a recipient of this award is as follows: Doctorate in Business Administration.

**The Open University** (**OU**) is a public distance learning and research university, and the biggest university in the UK for undergraduate education. The majority of the OU's undergraduate students are based in the United Kingdom and principally study off-campus; many of its courses can also be studied anywhere in the world. There are also a number of full-time postgraduate research students based on the 48-hectare university campus where they use the OU facilities for research, as well as more than 1,000 members of academic and research staff and over 2,500 administrative, operational and support staff.

A sculpture by Peter Sales was unveiled at the university 13 March 2012. It is entitled "Willmore Surface" and depicts a 4-lobed Willmore torus.^{ [1] }

- Willmore, T. J. (June 1959).
*An Introduction to Differential Geometry*. Oxford University Press. ISBN 0-19-853125-7. - Ruse, H. S.; Walker, A. G.; Willmore, T. J. (1961).
*Harmonic Spaces*. Edizioni Cremonese. - Willmore, T. J.; Hitchin, N (February 1984).
*Global Riemannian Geometry*. Ellis Horwood. ISBN 0-13-357583-7. - Willmore, T. J. (August 1997).
*Riemannian Geometry*. Oxford University Press. ISBN 0-19-851492-1.

**Differential geometry** is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.

**Karl Wilhelm Julius Hugo Riemann** was a German music theorist and composer.

**Kunihiko Kodaira** was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese national to receive this honour.

**John David Barrow** is an English cosmologist, theoretical physicist, and mathematician. Most recently, he served as Gresham Professor of Geometry at Gresham College from 2008 to 2011. Barrow is also a writer of popular science and an amateur playwright.

**John William Scott** "**Ian**" **Cassels**, FRS was a British mathematician.

**Richard Melvin Schoen** is an American mathematician known for his work in differential geometry.

**Richard Samuel Ward** FRS is a British mathematical physicist. He is a Professor of Theoretical Physics at the University of Durham.

The mathematician **Shmuel Aaron Weinberger** is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was, from 1994 to 1996, the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, and he is currently the Andrew MacLeish Professor of Mathematics and chair of the Mathematics department at the University of Chicago.

In mathematics, a **weakly symmetric space** is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian manifolds such that any two points can be exchanged by an isometry, the symmetric case being when the isometry is required to have period two. The classification of weakly symmetric spaces relies on that of periodic automorphisms of complex semisimple Lie algebras. They provide examples of Gelfand pairs, although the corresponding theory of spherical functions in harmonic analysis, known for symmetric spaces, has not yet been developed.

**Neo-Riemannian theory** is a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer. What binds these ideas is a central commitment to relating harmonies directly to each other, without necessary reference to a tonic. Initially, those harmonies were major and minor triads; subsequently, neo-Riemannian theory was extended to standard dissonant sonorities as well. Harmonic proximity is characteristically gauged by efficiency of voice leading. Thus, C major and E minor triads are close by virtue of requiring only a single semitonal shift to move from one to the other. Motion between proximate harmonies is described by simple transformations. For example, motion between a C major and E minor triad, in either direction, is executed by an "L" transformation. Extended progressions of harmonies are characteristically displayed on a geometric plane, or map, which portrays the entire system of harmonic relations. Where consensus is lacking is on the question of what is most central to the theory: smooth voice leading, transformations, or the system of relations that is mapped by the geometries. The theory is often invoked when analyzing harmonic practices within the Late Romantic period characterized by a high degree of chromaticism, including work of Schubert, Liszt, Wagner and Bruckner.

**Mikhail "Mischa" Katz** is an Israeli mathematician, a professor of mathematics at Bar-Ilan University. His main interests are differential geometry, geometric topology and mathematics education; he is the author of the book *Systolic Geometry and Topology*, which is mainly about systolic geometry. The Katz–Sabourau inequality is named after him and Stéphane Sabourau.

**Stephen Semmes** is Noah Harding Professor of Mathematics at Rice University. He is known for contributions to analysis on metric spaces, as well as harmonic analysis, complex variables, partial differential equations, and differential geometry. He received his B.S. at the age of 18, a Ph.D. at 21 and became a full professor at Rice at 25.

**Kenji Fukaya** is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the Fukaya category. He is a permanent faculty member at the Simons Center for Geometry and Physics and a professor of mathematics at Stony Brook University.

**Jürgen Jost** is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.

**Joseph Albert Wolf** is an American mathematician. He is now professor emeritus at the University of California, Berkeley.

**Richard Lawrence Bishop** is an American mathematician, a professor emeritus of mathematics at the University of Illinois at Urbana–Champaign. The Bishop–Gromov inequality in Riemannian geometry is named after him.

**Pertti Mattila** is a Finnish mathematician working in geometric measure theory, complex analysis and harmonic analysis. He is Professor of Mathematics in the Department of Mathematics and Statistics at the University of Helsinki, Finland.

**Sigmundur Gudmundsson** is an Icelandic-Swedish mathematician working at Lund University in the fields of differential geometry and global analysis. He is mainly interested in the geometric aspects of harmonic maps and harmonic morphisms. His work is partially devoted to the existence theory of complex-valued harmonic morphisms from Riemannian homogeneous spaces of various types, such as symmetric spaces and semisimple, solvable and nilpotent Lie groups.

Professor **John C. Wood** is a British mathematician working at the University of Leeds. He is one of the leading experts on harmonic maps and harmonic morphisms in the field of differential geometry.

Dr **Harold Stanley Ruse** MA FRSE was an English mathematician, noteworthy for the development of the concept of locally harmonic spaces.

- ↑ University of Durham News Item 29 Feb 2012

- University News, Durham University, 24 February 2005
- "Tom Willmore – Comment",
*The Times*, 3 May 2005 - "A Passion for Mathematics" by David Bomgardner, Durham University, 30 August 2005

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