Professor Simon Scott
Telephone: +44 020 7848 2778
Email: simon.scott@kcl.ac.uk
Office: S4.33, Strand Building, Strand Campus
Title: Professor in Analysis
Personal Website
Biography
Professor Simon Scott received his D.Phil. (doctorate) from the University of Oxford in 1993 under the supervision of Graeme Segal (FRS). He held positions at Oxford University, at the Universidad de los Andes (Bogotá), and at SISSA (Trieste), before moving to King's in 1998.
His research area is in geometric analysis, which is concerned with constructing invariants of manifolds via the study of partial differential equations. This relates information from the spectra of elliptic pseudodifferential operators to the topology and geometry of the space over which the operator is defined, and has important applications to a number of areas of mathematics as well as to the physics of quantum fields.
Professor Scott is the author of a number of research and expository articles, as well as a major research book on traces and determinants of pseudodifferential operators.
Research Interests
His research interests concern how certain partial differential equations defined over a curved n-dimensional space (manifold) intertwine geometric and topological invariants into spectral generating functions. Roughly speaking, the idea is that although the individual eigenvalues of a Dirac-Laplacian (say) are generally impossible to compute, if one takes them all together built into a suitable zeta function then together they relate local geometric data (curvature and other metric tensors) to preferred global topological invariants of the space. In principal those topological invariants correspond to certain quantum numbers and there is consequently a hugely diverse and active research effort going on to understand how this relates to quantum field theory.
On the pure analysis side, he is currently particularly interested in Arthur-Selberg trace formulae and regularized trace invariants of Fourier integral operators. On the other hand, he has an ongoing research programme into logarithmic structures in topological quantum field theory and how these defined an intriguing deep underlying framework of additive invariants for such theories.
He is in the process of building-up a new geometric analysis group at King’s, an important research area internationally but quite unrepresented in the UK, and so would welcome enquiries from prospective post-docs, PhD students and collaborators interested in being a part of this new group.
Selection of Publications
The following are a selection of research and expository works:
Traces and Determinants of Pseudodifferential Operators. Published September 2010 by OUP http://ukcatalogue.oup.com/product/9780198568360.do
Eta forms and determinant lines Advances in Mathematics. 225, pp. 2517- 2545 (2010). PDF
Logarithmic structures and TQFT Expository article in Clay Mathematics Proceedings, volume 12 ( 2011). PDF
The Quillen Determinant An expository article for "The Encyclopedia of Mathematical Physics", Elsevier Press. PDF
The residue determinant Comm. PDES, 30, pp 483-507, (2005). PDF
Zeta forms and the local family index theorem Trans. Amer. Math. Soc. 359, 1925-1957, (2007). PDF