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Professor Alice Rogers OBE

AliceRogersTelephone: +44 020 7848 2242

Email: alice.rogers@kcl.ac.uk

Office: K4U.27, Strand Building, Strand Campus

Title:  Emeritus Professor of Mathematics

Personal Website

Biography

Alice Rogers first joined the KCL Mathematics Department in 1983 as a Research Associate with Professor JG Taylor. From 1984-1989 she held an EPSRC Advanced Research Fellowship and from 1989-1994 a Royal Society University Research Fellowship. Since 1994 she has been in turn lecturer, reader and professor of mathematics. She obtained a Ph.D. from Imperial College in 1981 with a thesis on supermanifolds. Her first degree is in mathematics from the University of Cambridge.

Alice Rogers’ publications relate to geometrical and analytic aspects of supermanifolds together with applications in theoretical physics, and she is the author of a book with the title ‘Supermanifolds: Theory and Applications’.

From 2001 until 2004 Alice Rogers was Head of Department. More recently, as a member of the Advisory Committee on Mathematics Education, she has been involved in national education policy. She is a Governor of the King’s College London Mathematics School.

Research Interests

Alice's research concerns supermanifolds and their applications in theoretical physics. A supermanifold is a space with some commuting and some anticommuting coordinates.  An account of the theory of supermanifolds, together with applications of these spaces, is given in the book Supermanifolds: theory and applications

Her more recent work relates to the theory of path integration on supermanifolds which she developed, building on the standard approach to path integration on Riemann manifolds. The motivation for this work is to bring mathematical rigour in a direct way into the heuristically powerful physicists' path integral approach. These methods give information about the evolution operator in supersymmetric quantum mechanics, and have many geometric applications, for instance to the Atiyah-Singer index theorem.  Additionally, and this is the area of her most recent work, these techniques allow a more complete understanding of the quantization of theories with symmetries.

Selection of Publications

  • A Global Theory of Supermanifolds, Journal of Mathematical Physics 21:1352-1365 (1980), http://link.aip.org/link/doi/10.1063/1.524585
  • Supersymmetry and Brownian motion on supermanifolds: a survey article on her work on path integration in superspace.
  • Gauge fixing and BFV quantization. Classical and Quantum Gravity 17:389-397, 2000: where supertrace arguments are used to show how the BRST commutator term in the Hamiltonian regularises the path integral.
  • The topological particle and Morse theory. Classical and Quantum Gravity  17:3703-3714, 2000: in which it is shown that the supersymmetric model used by Witten in his celebrated paper on Morse theory can be obtained by BRST quantisation of the topological particle, and the tunelling calculations for the model are carried out rigorously using a new stochastic calculus technique, which incidentally show why the WKB method for quantum tunelling has improved accuracy in supersymmetric theories.
  • Equivariant BRST quantization and reducible symmetries, J. Phys. A: Math. Theor. 40 (2007) 4649-4663 : a paper which extends the standard BRST quantization of Hamiltonian systems with symmetry to systems with reducible symmetry.

 

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