Workshop: Geometry and Physics

This IGA workshop, marking Keith Hannabuss's 60th birthday, is in honour of his key contributions to mathematical physics. Keith completed his DPhil on quantum theory in de Sitter spacetime in 1969 with John Lewis as his supervisor at Oxford.

He then had a junior research fellowship at Magdalen College (Oxford) and also spent a year as a Moore Instructor at MIT. Keith commenced his permanent appointment at Balliol College (Oxford) in 1972, and his first DPhil student was Alan Carey. This started Keith's long association with Australia, where he has frequently visited and has had several collaborators, especially at the University of Adelaide, collaborating on integrable systems, quantum Hall effect and duality in string theory.

Titles and abstracts

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

Schedule

Refreshments: These will be available to participants at EM117

Participant information

Venue

Engineering and Mathematics building, EMG07 (see campus map).

Registration and funding

There will be no registration fees: all are welcome. The workshop is funded by the Institute of Geometry and its applications (IGA).

Organiser