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New Connections in Geometry and Mathematical Physics

Project ID: 2531ad1555

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Research Theme: Mathematical Sciences

UCL Lead department: Mathematics

Department Website

Lead Supervisor: Rod Halburd

Project Summary:

The aim of this project is to pursue new developments within the fields of geometry, topology, dynamical systems, general relativity, and integrable systems; and especially to develop new links between these fields.

Specific themes in geometry that may be covered include gauge theory, calibrated geometry, geometric measure theory, geometric representation theory and the geometric Langlands programme, symplectic topology, moduli spaces, geometric group theory, birational geometry, and derived categories.

Within general relativity, research will focus on (i) modifications of the Einstein-Hilbert action, and (ii) the use of dynamical systems in cosmology. In integrable systems, topics may include the Korteweg–de Vries equation and the Sine-Gordon equation, and their study with geometric techniques.