Workshop: Differential Geometry

The Institute for Geometry and its Applications, the University of Adelaide, is hosting a Workshop on Differential Geometry to be held in the Flentje lecture theatre on Monday 2nd December 1996.

Titles and abstracts

Robin Graham (University of Washington)

The FBI transform

The FBI (Fourier-Bros-Iagolnitzer) transform is a modification of the Fourier transform which is especially useful for detecting and studying local real-analyticity of functions on R^n. The standard use of the Fourier transform to study C-infinity regularity will be recalled, and its inadequacy for the study of real analyticity will be explained. The FBI transform will be defined and its use in studying real-analyticity will be discussed.

Jan Slovak (University of Adelaide and Masaryk University, Brno)

Ehresmann's approach to connections

In this quite general and introductory talk, I will focus on the most general approaches to connections, curvature, and parallel transport, without any linearity, structure groups, etcetera. Links to the more standard concepts of linear and principal connections will be given.

Break

Michael Murray (University of Adelaide)

Characteristic Classes and Classifying Spaces

I will give an elementary account of the theory of classifying spaces and characteristic classes. The emphasis will be on examples so as to motivate Milnor's construction of the classifying space BG of a topological group G. You do not need to bring your own 3D glasses---they will be provided.

Patrick Doran-Wu (University of Adelaide)

Using a standard form algorithm to tackle the Einstein-Weyl equations

Lunch

Michael Eastwood (University of Adelaide)

Envelopes of holomorphy

A major difference between holomorphic functions of one variable and of several (i.e. more than one) is that a holomorphic function of several variables is apt automatically to extend to a larger set than where it is originally defined. I shall present some examples of this phenomenon.

Vladimir Ezhov (University of Adelaide)

Local and global holomorphic equivalence of pseudoconvex hypersurfaces and higher codimensional C-R manifolds

I'll explain how the theory of normal forms and just qualitive geometrical analysis of ODE enables one to prove a formerly complicated theorem about global extension of local holomorphic equivalence for compact real analytic strictly pseudoconvex hypersurfaces in complex manifolds. This problem is awaiting a generalization for higher codimensional CR manifolds. I'll discuss a couple of examples that prevent the direct generalization of the above theorem.

Bryan Wang (University of Adelaide)

Floer Homology Theory

I will discuss Floer-type homology theory for Seiberg-Witten monopoles and its relationships with SW invariants.

Break

John Rice (Flinders University)

Lowest K-types and geometric quantisation

Keith Hannabuss (University of Oxford)

The asymptotics of quantisation on Kaehler manifolds

Drinks in the Staff Club