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Colloquium talks will take place some Tuesdays at 4.00 pm in Room 505 on the 5th floor of the mathematics department. See how to find us for further details. There will be tea afterwards in room 606.
If you require any more information on these talks, please contact either Dr Nadia Sidorova (e-mail: n.sidorova AT ucl.ac.uk or tel: 020-7679-7864) or Professor Yaroslav Kurylev (e-mail: y.kurylev AT ucl.ac.uk or tel: 020-7679-7896).
26 October 2010
John Ball - Oxford University
Partial regularity and smooth topology-preserving approximation of rough domains
Abstract:
The talk concerns bounded domains with continuous boundary. We study how the corresponding `good direction', with respect to which the boundary is locally a graph of a continuous function, varies in a neighbourhood of the boundary, and thus show how such domains can be approximated both from the inside and the outside by homotopically equivalent smooth domains. The good directions form a globally-defined field that carries
some topological information about the domain, which we explore. Finally we describe a surprising consequence of the study, that the domain has portions of the boundary with better regularity. This is joint work with Arghir Zarnescu.
14 December 2010
Brian Davies - King's College London
Eigenvalues and Resonances of Continuous Graphs
Abstract:
The lecture will present an account of eigenvalues and resonances of continuous (also called quantum) graphs that depends only on the analysis of some finite matrices and a theorem of Langer in 1931 on the zeros of some simple analytic functions. This may help to motivate those who wish to understand technically harder results in the field.