| Mathematics Department |
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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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| 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. | |
| 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. | |
| 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. | |
| The Quillen Determinant. An expository article for 'The Encyclopedia of Mathematical Physics', Elsevier Press. | |
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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. |
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| 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. | |
| 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. | |
| 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. | |
| Zeta determinants on manifolds with boundary. In this paper a general framework is given for understanding regularized determinants for APS boundary problems. | |
| 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. | |
| 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. | |
| Zeta-determinant on the space of elliptic self-adjoint boundary conditions. Joint with Krzysztof Wojciechowski. A short announcement of the relative zeta determinant formula. | |
| 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. | |
| 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. | |
| 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. | |
| On Chern-Weil forms associated with superconnections. Joint with Sylvie Paycha. Constructing characteristic classes using zeta regularization for families of Dirac operators. | |
| 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. | |
| Eta forms and the Chern character. An approach to families index theorem for families of Dirac operators on manifolds with boundary. | |
| 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. | |
| 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. | |
| 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. | |
| Restricted Grassmannians. Some notes on the manifold structure of infinite restricted Grassmannians and associated index theory. | |
| Determinants of elliptic boundary value problems in quantum field theory. Joint with Krzysztof Wojciechowski. An expository article for a conference proceedings. | |
| Determinants of Dirac Boundary Value Problems over Odd-dimensional Manifolds. Work on determinant line bundles for elliptic boundary problems. | |
| Determinants, Grassmannians and elliptic boundary value problems for the Dirac operator. Joint with Krzysztof Wojciechowski. An early account of the relative zeta determinant on the restricted Grassmannian. | |
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Determinants, manifolds with boundary and Dirac operators. Joint with K.Wojciechowski, G.Morchio, B.Bavnbek. |
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| Some notes on geometry and quantization Some notes from a short lecture course. |
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This document was last modified on Oct 13 17:05:44 1998