Mathematics Department

Photograph
Prof. Simon Scott 
Department of Mathematics
King's College London
Strand, London WC2R 2LS
United Kingdom
Room 433, Strand Building
Tel: +44-(0)20-7848 2778 (direct)
Tel: +44-(0)20-7848 2828 (general office)
Fax: +44-(0)20-7848 2017
E-mail: simon.scott@kcl.ac.uk
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Current PhD students:
Elisabeth Grieger
Philip Johnson

If you are graduating soon then you are strongly advised to come to King's to do your doctorate or Post-doc in geometric analysis.  Information 

Research:



Traces and Determinants of Pseudodifferential Operators.  Oxford Mathematical Monographs, OUP. 1.OUP website
2.Front Matter

3.Introduction
Eta forms and determinant lines. On the zeta function metric and curvature for a family of Dirac operators on a compact manifold with boundary. PDF
Characteristic classes and zeroth order pseudodifferential operators. Joint with  Andres Larrain-Hubach, Steve Rosenberg, Fabian Torres-Ardila. A summary of ongoing work on Chern classes defined by exotic traces. PDF
Logarithmic structures and TQFT.   This is an expository article on logarithmic structures on semi-groups and categories and the extension of this construction to topological field theories. PDF
The Quillen Determinant. An expository article for 'The Encyclopedia of Mathematical Physics', Elsevier Press. PDF

The residue determinant.  In this article it is shown that the residue trace on the algebra of integer order classical pseudodifferential operators leads to an exotic determinant there.

PDF
Zeta forms and the local family index theorem. Invariants in geometric analysis for a single operator  have analogues for families of operators, here this is worked out for the complex powers PDF
A Laurent expansion for regularized integrals of holomorphic symbols. Joint with Sylvie Paycha. Here, a detailed analysis is made of the pole structure for spectral zeta functions. PDF
Laurent expansion for holomorphic families of log-polyhomogeneous symbols. Joint with Sylvie Paycha. The analysis in the above article is extended to logarithmic pseudodifferential operators. PDF
Zeta determinants on manifolds with boundary. In this paper a general framework is given for understanding regularized determinants for APS boundary problems.    PDF
A Symbol Proof of the Local Index Theorem.  Joint with Don Zagier. Here the residue determinant formula for the index of an elliptic pseudodifferential operator is  used to compute the analytic (or `local') Atiyah-Singer index density PDF
The zeta-determinant and Quillen determinant over odd dimensional manifolds. Joint with Krzysztof Wojciechowski.  A basic formula for relative zeta determinants in terms of boundary Fredholm determinants.  PDF
Zeta-determinant on the space of elliptic self-adjoint  boundary conditions. Joint with Krzysztof Wojciechowski. A short announcement of the relative zeta determinant formula.  PDF
The unitary twist method for computing regularized determiants in dimension one. This is a general account (recently latexed from its hand written form) of the determinant computation in dim 1 with self adjoint boundary conditions using resolvent and heat trace methods, motivating the (published) note below PDF
The zeta-determinant and  C-determinant in dimension one.  A short joint note (in LMP) with  Bernhelm Booss-Bavnbek and Krzysztof Wojciechowski. One can generally compute spectral invariants in dim 1 explicitly and this is carried out here for the zeta determinant in a simple case.  PDF
Analysis of elliptic families in dimension one. Dimension one provides a model case where zeta function computations be obtained very explicitly. Here we work out the metric and curvature formulae, obtained in full generality in `Eta forms and determinant lines' (above) for higher dimensions. PDF
On Chern-Weil forms associated with superconnections. Joint with Sylvie Paycha. Constructing characteristic classes using zeta regularization for families of Dirac operators.  PDF
CPn instantons and the Atiyah-Singer family's index theorem. In case the moduli space has dimension zero and is compact then it is a finite numder of points, and the topological RRH families index theorem can be used to compute that number. PDF
Eta forms and the Chern character. An approach to families index theorem for families of Dirac operators on manifolds with boundary. PDF
Splitting the curvature of the determinant line bundle. There is a connection and metric on the deteminant bundle for a family of first order elliptic operators associated to each emebedded codimension zero submanifold, whose curvature is functorial with respect to sewing.   PDF
Functorial quantum field theory, gauge anomalies and the Dirac determinant bundle. Joint with Jouko Mickelsson.  In  this article a projective representation of a cobordism category is constructed, corresponding to topological QFT (Feynam path integral) structures.   PDF
Relative zeta determinants and the geometry of the determinant line bundle. A brief account of how the canonical metric and connection associated to an embedded codimension zero submanifold relates to the zeta regularized metric and connection. PDF
Restricted Grassmannians.  Some notes on the manifold structure of infinite restricted Grassmannians and associated index theory. PDF
Determinants of elliptic boundary value problems in quantum field theory.  Joint with Krzysztof Wojciechowski.  An expository article for a conference proceedings PDF
Determinants of Dirac Boundary Value Problems over Odd-dimensional Manifolds. Work on determinant line bundles for elliptic boundary problems. PDF
Determinants, Grassmannians and elliptic boundary value problems for the Dirac  operator. Joint with  Krzysztof WojciechowskiAn early account of the relative zeta determinant on the restricted Grassmannian.  PDF

Determinants, manifolds with boundary and Dirac operators. Joint with K.Wojciechowski, G.Morchio, B.Bavnbek.  

PDF
Some notes on geometry and quantization   Some notes from a short lecture course. PDF






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This document was last modified on Oct 13 17:05:44 1998