Prof. Peter Bouwknegt, (ANU)  
  "Generalized Geometry and Applications" I,II,III

Scheduled on 16-18, Nov. 10:30-12:00

Abstract: 
Geometry is one of the pillars of both ancient and modern mathematics, 
and plays a vital role in many scientific applications, in particular 
in physics.  In the past two decades it has become clear, mainly by 
studying duality symmetries in Quantum Field Theory and String Theory, 
that there exists an important generalization of classical differential 
geometry. Recently, the axioms for this "Generalized Geometry" were 
introduced by Hitchin and his students. In these lectures I will explain 
the basics behind Generalized Geometry. Generalized Geometry cuts through 
many disciplines in Mathematics, such as symplectic geometry, complex 
geometry, differential geometry and algebra.  The lectures will therefore 
be interesting to a broad audience of mathematicians and mathematical 
physicists.  The lectures will be presented at an elementary level and 
will be suitable for postgraduate students. Topics to be covered include 
Lie and Courant algebroids, generalized complex manifolds, generalized 
Kahler manifolds, etc, as well as applications, mostly in the context 
of String Theory. 

Prof. Mathai Varghese,(Adelaide) 
  "T-duality and Noncommutative Geometry", I,II 

Scheduled on 17,18, Nov. 14:30-16:00

Abstract:
When spacetime is a principal torus bundle with background flux, and one 
tries to iterate T-duality for circle bundles (as proved with Bouwknegt 
and Evslin) one circle at a time, some of the circles tend to mysteriously 
disappear, thereby preventing one from obtaining a classical T-dual. 
In this lecture, I will talk about how the use of noncommutative geometry 
solves the problem of the missing T-duals. The T-dual in this case is a 
C*-bundle over the base space with fibres noncommutative tori with varying 
noncommutative parameter  in the base direction. This is joint work with 
J. Rosenberg.

16 Nov. 15:00-16:00
Prof. Mathai Varghese, 

Title: The index theorem for projective families of elliptic operators

Abstract: I will talk about ongoing research with Melrose and Singer on 
the index theorem for projective families of elliptic operators. Some 
natural examples will also be included.

16 Nov. 16:10-17:10
Prof. Peter Bouwknegt,
Title:D-branes on group manifolds, (twisted) K-theory and the Verlinde
algebra

Abstract:
In this talk I will briefly review why charges of D-branes are classified 
by (twisted) K-theory, and in particular will elaborate on the case of 
D-branes on group manifolds. I will discuss explicit results for the 
twisted K-theory of compact, simple, groups and the relation to the 
Verlinde algebra.