Speaker: Peter Bouwknegt
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
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
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
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