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All colloquia (unless otherwise stated) will take place on Tuesdays at 4.00pm in Room 500 which is located on the 5th floor of the Mathematics Department. See How to Find Us for further details. There will be tea afterwards in Maths Room 502. If you require any more information on the Departmental Colloquia please contact Prof Dima Vassiliev e-mail: d.vassiliev AT ucl.ac.uk or tel: 020-7679-2442.
11 February 2014
Please note: This talk will start at 4:30pm.
Nigel Hitchin - University of Oxford
Title: Complex and quaternionic differential geometry
Abstract:
The differential geometry of complex manifolds is usually approached through the study of K\"ahler manifolds. These are Riemannian manifolds with holonomy in the unitary group $U(m)$. But there are other structures which are also interesting and one of these is the class of manifolds with a torsion-free connection having holonomy in the noncompact real Lie group $U^*(2m)$.
In this geometry one can discuss geodesics and the notion of volume but there is in general no concept of distance. However, they occur quite naturally associated to other differential-geometric structures related to the quaternions and in particular there are links to the so-called c-map in string theory.
The talk will focus on these new approaches and examples.