# Dr Graeme Segal

## BSc, MA, DPhil, FRS

## Emeritus Fellow since 2009

### Contact by email

### Background

- Senior Research Fellow, All Souls College, Oxford (from 1999 to 2009)
- Lowndean Professor of Astronomy and Geometry, and Fellow of St John’s College, Cambridge (from 1990 to 1999)
- Oxford University: Junior Lecturer in Mathematics (1965-6); CUF Lecturer (1966-70); Science Research Council Research Associate (1971-5); University Lecturer (1975-8); Reader (1978-89); Professor of Mathematics (ad hominem) (1989-90) (from 1965 to 1990)
- Fellow, St Catherine’s College, Oxford (from 1966 to 1990)
- Junior Research Fellow, Worcester College, Oxford (from 1964 to 1966)
- Graduate student, Balliol College, Oxford (from 1963 to 1964)
- Graduate student, St. John’s College, Cambridge (from 1962 to 1963)
- Undergraduate, University of Sydney (from 1958 to 1961)

### Research interests

- Geometry: algebraic topology and the structure of manifolds
- Quantum field theory: its conceptual and mathematical structure; geometric applications of field theory; two-dimensional conformal field theory
- Global analysis: index theory, geometry and representations of finite- and infinite-dimensional Lie groups; integrable systems

### Selected publications

*Space and spaces*, Presidential Lecture to the London Mathematical So-

ciety, November 2013.*A geometric perspective on quantum field theory*. Contemp. Mathematics,

620 (2014), pp. 281-294.*Reflections on Quillen's work on algebraic K-theory*. Quarterly J. Math.,

64 (2013), pp. 645-664.*Locality of holomorphic bundles, and locality in quantum field theory*. In

*The many facets of geometry*, ed. O. Garcia-Prada et al., OUP 2010, pp.

164-176.- ‘The definition of conformal field theory’, in U. Tillmann (ed.),
*Topolology, geometry, and quantum field theory* (CUP, 2004) - (with A. Pressley),
*Loop groups* (OUP, 1986) - ‘Loop groups and equations of KdV type’,
*IHES Publ. Math.*, 61 (1985), 5-65 - ‘Unitary representations of some infinite-dimensional groups’,
*Comm. Math. Phys.*, 80 (1981), 301-42 - ‘The topology of spaces of rational functions’,
*Acta Mathematica*, 143 (1979), 39-72 - ‘Categories and cohomology theories’,
*Topology*, 13 (1974), 293-312 - Link to publications

### Other professional memberships and roles

- Editor,
*Topology* (from 1970 to 1990) - Member, Institute for Advanced Study (from 1969 to 1970)