Speaker: Peter Bouwknegt

Title: Generalized Geometry, Mirror Symmetry and T-duality

Abstract: We will review the definition and motivation behind the construction of generalized complex manifolds, generalized Kahler manifolds, generalized Calabi-Yau manifolds, ... etc, in the sense of Hitchin and Gualtieri.  We will show how these structures can be twisted by a gerbe, and discuss applications to mirror symmetry and T-duality in the presence of background fluxes.

Speaker: Nicholas Buchdahl

Title: A new result in the classification of complex surfaces

Abstract: It is widely accepted that the one remaining gap in the Enriques-Kodaira classification of compact complex surfaces is in the complete determination of all the surfaces of class VII with positive second Betti number. Very recently, Andrei Teleman has proved a result which determines the surfaces with second Betti number 1 in this class. His proof, which is an echo of Simon Donaldson's first main theorem on smooth 4-manifolds, is an extremely elegant application of gauge theory combined with algebro-geometric arguments. In my talk, I will describe some of the background to this classification problem and give an outline of Teleman's proof.

Speaker: Michael Eastwood

Title: A New Homogeneous Tube Domain

Abstract: Recent work with Vladimir Ezhov and Alexander Isaev found some new homogeneous tube domains in C^4 and I shall discuss one of them in relation to other well-known homogeneous tubes. No prior knowledge of tubes will be assumed.

Speaker: Keith Hannabuss

Title: Quantum fluids, integrable systems, and Weyl's character formula

Abstract: It has been suggested that the fractional Quantum Hall Effect can be modelled by incompressible fluid flow in a non-commutative plane. Physical and mathematical considerations link this to the Calogero-Moser integrable model. This leads via symplectic geometry and group representation theory to a slightly different perspective on Weyl's character formula.

Speaker: Mathai Varghese

Title: Towards the fractional quantum Hall effect via noncommutative geometry