nLab Graeme Segal

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George Bergman

in 1982

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Selected writings

On classifying spaces and spectral sequences (and introducing, following Grothendicek 61, the “Segal conditions”, see also at complete Segal space):

• Graeme Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math., vol. 34, pp. 105–112 (1968)

On the representation rings of compact Lie groups:

• Graeme Segal, The representation ring of a compact Lie group, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, January 1968, Volume 34, Issue 1, pp 113-128 (numdam:PMIHES_1968__34__113_0)

On equivariant K-theory:

• Graeme Segal, Equivariant K-theory, Inst. Hautes Etudes Sci. Publ. Math. 34 (1968) 129-151 [numdam:PMIHES_1968__34__129_0]

On the Atiyah-Segal completion theorem:

• Michael Atiyah, Graeme Segal, Equivariant $K$-theory and completion, J. Differential Geom. Volume 3, Number 1-2 (1969) 1-18 [euclid:jdg/1214428815]

On equivariant stable homotopy theory and the isomorphism between the Burnside ring and the equivariant stable Cohomotopy of the point:

• Graeme Segal, Equivariant stable homotopy theory, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, Gauthier-Villars, Paris (1971) 59-63 [pdf]

On configuration spaces of points from iterated loop spaces:

• Graeme Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213–221. MR 0331377 (pdf)

On the Kahn-Priddy theorem (and a pre-cursor of Snaith's theorem):

• Graeme Segal, The stable homotopy of complex of projective space, The quarterly journal of mathematics (1973) 24 (1): 1-5. (pdf, doi:10.1093/qmath/24.1.1)

On K-theory of permutative categories, Gamma spaces as models for connective spectra, and the identification of stable Cohomotopy with the K-theory of finite sets:

• Graeme Segal, Categories and cohomology theories, Topology vol 13, pp. 293-312, 1974 (doi:10.1016/0040-9383(74)90022-6, pdf)

On the group completion theorem:

• Dusa McDuff, Graeme Segal, Homology fibrations and the “group-completion” theorem, Invent. Math. 31 3 (1976) 279-284 [doi:10.1007/BF01403148]

On equivariant homotopy theory motivated by equivariant iterated loop spaces and configuration spaces of points:

• Graeme Segal, Some results in equivariant homotopy theory (1978) [scan: web, pdf]

Proving the equivariant Whitehead theorem:

• Ioan James, Graeme Segal, Theorem 1.1 in: On equivariant homotopy type, Topology 17 3 (1978) 267-272 [doi:10.1016/0040-9383(78)90030-7]

On the homotopy type of spaces of rational functions from the Riemann sphere to itself (related to the moduli space of monopoles in $\mathbb{R}^3$ and to the configuration space of points in $\mathbb{R}^2$):

• Graeme Segal, The topology of spaces of rational functions, Acta Math. 143 (1979) 39-72 [euclid:1485890033]

• Ralph L. Cohen, John D. S. Jones, Graeme B. Segal, Stability for holomorphic spheres and Morse theory, in: K. Grove, I. H. Madsen, E. K. Pedersen (eds.) Geometry and Topology: Aarhus, Contemporary Mathematics

  Volume: 258; (arXiv:math/9904185, ISBN:978-0-8218-2158-9)

On the ordinary cohomology of the moduli space of Yang-Mills monopoles:

• Graeme Segal, Alex Selby, The cohomology of the space of magnetic monopoles, Commun. Math. Phys. 177, 775–787 (1996) (doi:10.1007/BF02099547)

On equivariant bundles with abelian structure group:

• Richard Lashof, Peter May, Graeme Segal, Equivariant bundles with abelian structural group, Contemporary Mathematics 19, 1983 (doi:10.1090/conm/019, pdf, pdf)

On loop groups of compact Lie groups and their Kac-Moody group central extension:

• Andrew Pressley, Graeme Segal, Loop groups, Oxford University Press (1988)

• Graeme Segal, Loop groups (pdf)

On integrable functions in terms of infinitedimensional Sato-Segal-Wilson Grassmannian

• G. Segal, George Wilson, Loop groups and equations of KdV type, Publ. Math. IHÉS 61, 5–65 (1985) numdam MR87b:58039 Zbl0592.35112

On 2d conformal field theory and modular functors:

• Graeme Segal, Two-dimensional conformal field theories and modular functors, in: IXth International Congress on Mathematical Physics, Swansea 1988, Adam Hilger, Bristol and New York (1989) 22–37 [pdf, pdf]

Further on the functorial-definition of 2d conformal field theory:

• Graeme Segal, The definition of conformal field theory, in: K. Bleuler, M. Werner (eds.), Differential geometrical methods in theoretical physics (Proceedings of Research Workshop, Como 1987), NATO Adv. Sci. Inst., Ser. C: Math. Phys. Sci. 250 Kluwer Acad. Publ., Dordrecht (1988) 165-171 [doi:10.1007/978-94-015-7809-7]

• Graeme Segal, The definition of conformal field theory, in: Ulrike Tillmann (ed.), Topology, geometry and quantum field theory , London Math. Soc. Lect. Note Ser. 308, Cambridge University Press (2004) 421-577 [doi:10.1017/CBO9780511526398.019, pdf, pdf]

On twisted K-theory and twisted equivariant K-theory:

• Michael Atiyah, Graeme Segal, Twisted K-theory, Ukrainian Math. Bull. 1, 3 (2004) (arXiv:math/0407054, journal page, published pdf)

• Michael Atiyah, Graeme Segal, Twisted K-theory and cohomology (arXiv:math/0510674)

On quantization of the electromagnetic field in view of Dirac charge quantization and higher U(1)-gauge theory:

• Daniel S. Freed, Gregory W. Moore, Graeme Segal, p. 7 of: The Uncertainty of Fluxes, Commun. Math. Phys. 271:247-274, 2007 (arXiv:hep-th/0605198, doi:10.1007/s00220-006-0181-3)

• Daniel Freed, Gregory Moore, Graeme Segal, Heisenberg Groups and Noncommutative Fluxes, Annals Phys. 322:236-285 (2007) (arXiv:hep-th/0605200)

On Wick rotation in quantum field theory in terms of complex metrics:

• Maxim Kontsevich, Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, The Quarterly Journal of Mathematics 72 1-2, (2021) 673–699 [arXiv:2105.10161, doi:10.1093/qmath/haab027]

review talks:

• Graeme Segal, Wick rotation and the positivity of energy in quantum field theory, talk at Institut des Hautes Études Scientifiques (IHÉS), June 2014 (video recording)

• Graeme Segal, Wick Rotation and the Positivity of Energy in Quantum Field Theory, talk at IAS Physics Group Meeting, December 2021 (video recording)

On quantum field theory:

• Graeme Segal: A point of view on quantum field theory, lecture series at International Center for Mathematical Sciences (July 2024) [video: part 1, part 2, part 3, part 4]

category: people