Workshop: Strings and Mathematics 2004

String Theory is arguably the most exciting research area in modern mathematical physics. Prolific research is being carried out in String Theory world-over.

String Theory is known to the general public as the "Theory Of Everything", thanks to its great success in unifying Relativity and Quantum Field Theory, yielding a theory of Quantum Gravity.

The impact of String Theory is not just felt in physics, but also in modern mathematics. It has profound connections with a broad spectrum of modern mathematics, including algebraic geometry, differential geometry, noncommutative geometry, K-theory, index theory and representation theory. Research in String Theory has created several interesting open problems both in this rapidly developing field, and in the related areas of modern mathematics.

Titles and abstracts

Speaker: Jerry Kaminker (IUPUI)
Title: Noncommutative geometry and duality: the Baum-Connes map

Speaker: Jerry Kaminker (IUPUI)
Title: Hyperbolic dynamics and NCG

Speaker: Jouko Mickelsson (KTH Royal Institute of Technology, Sweden)
Title: From canonical quantization to gerbes
Abstract: This is a general introduction to how gerbes emerge in Quantum Field Theory, with links to the geometry of infinite-dimensional Grassmannians.

Speaker: Jouko Mickelsson (KTH Royal Institute of Technology, Sweden)
Title: Supersymmetric Wess-Zumino-Witten model, twisted K theory classes and their charges

Speaker: Michael Murray (U. Adelaide)
Title: The bundle gerbe over SU(n)
Abstract: There are a number of constructions of a gerbe or bundle gerbe over a compact Lie group. I will give a simple construction for the case of SU(n).

Speaker: Peter Bouwknegt (U. Adelaide)
Title: T-duality for principal torus bundles I
Abstract: T-duality, in its simplest form, is the R to 1/R symmetry of String Theory compactified on a circle of radius R. It can be generalized to manifolds which admit circle actions (e.g. circle bundles) or, more generally, torus actions. In the case of nontrivial torus bundles, and in the background of H-flux, T-duality relates manifolds of different topology and in particular provides isomorphisms between the twisted cohomologies and twisted K-theories of these manifolds. In this talk we will discuss these developments as well as provide some examples in the case of principal circle bundles. In a sequel to this talk Mathai will discuss the case of higher dimensional torii.

Speaker: Mathai Varghese (U. Adelaide)
Title: T-duality for principal torus bundles II
Abstract: My talk will cover the general case of T-duality for principal torus bundles. The new phenomenon that occurs here is that not all background fluxes are T-dualizable, and some joint work with Bouwknegt and Hannabuss works out the precise class of T-dualizable background fluxes. The isomophisms in twisted K-theory and twisted cohomology also follow in this case. A big puzzle remained to explain these mysterious ``missing T-duals'' corresponding to non-T-dualizable background fluxes. In another joint work with Rosenberg, we give a complete characterization of T-duality on principal 2-torus-bundles with background flux. Here we show that this problem is resolved using noncommutative topology. It turns out that every principal 2-torus-bundle with background flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. This suggests an unexpected link between classical string theories and the ``noncommutative'' ones, obtained by ``compactifying'' along noncommutative tori.

Speaker: Avijit Mukherjee (U. Adelaide)
Title: D-branes and Stability
Abstract: In this talk, we shall discuss the idea of Pi stability for the B-type D- branes on Calabi-Yau (CY) manifolds, adopting a description of these branes as being objects in a certain category. The stability of the D-branes is exhibited as a function of the CY moduli and this approach then enables us to work over the entire moduli space and not just at the large radius limit. The monodromy transformations are then realised as autoequivalences of these categories which via Orlov's theorem are then implemented by Fourier-Mukai transformations.

Speaker: Hisham Sati (U. Adelaide)
Title: Recent developments in M-Theory
Abstract: M-Theory is an eleven-dimensional theory that unifies the five consistent ten-dimensional Superstring theories. The theory has proved to have rich physical and mathematical structures that are not yet fully understood. In this talk I will review the basics of M-Theory and the recent developments in understanding this theory.

Speaker: Danny Stevenson (U. Adelaide)
Title: An elementary proof of Hodgkin's Theorem
Abstract: The K-theory of a compact Lie group G with torsion free fundamental group was computed by Hodgkin to be an exterior algebra over the integers on m generators where m is the rank of G. We will give an elementary proof of this fact. If time permits we will comment briefly on the twisted case (this last part is still work in progress).

Schedule

Participant information

Venue

NITP seminar room, 4th Floor, 10 Pulteney Street, Adelaide (see campus map)

For students:

Both of the organisers and some other staff in Adelaide, have projects related to String Theory for interested PhD or Honours students who would like to do research here in Adelaide. Amongst the talks will be some expository lectures, for students in both mathematics and mathematical physics, at the level of beginning postgraduate students. Reasonable financial support is available for interstate students.

Registration:

There is no registration. All are welcome.

Accommodation:

Contact one of the organizers to help arrange your accommodation for the workshop.

Information on Adelaide

• Destination Adelaide
• Tourism in Adelaide and surrounds
• Current weather and time in Adelaide

Organisers