Wed 
Feb. 12 
11:00  12:00 
Bernhard Lamel (University of Vienna) 
Symmetries of nonminimal hypersurfaces
Symmetries of real hypersurfaces (or, more generally, CR structures) are very restricted and have both interesting regularity properties and a rich structure theory, intimately related to the
question of the classification of these objects. In this talk we will survey some recent results on such symmetries in the nonminimal case, draw analogies to the minimal case, and point out the
stark differences which occur in this degenerate setting.

Thu 
Feb. 27 
4:00  5:00 
Karin Melnick (University of Maryland) 
(Colloquium) Normal forms for local flows on parabolic geometries
The exponential map in Riemannian geometry conjugates the differential of an isometry at a point with the action of the isometry near the point. It thus provides a linear normal
form for all isometries fixing a point. Conformal transformations are not linearizable in general. I will discuss a suite of normal forms theorems in conformal geometry and, more generally, for
parabolic geometries, a rich family of geometric structures of which conformal, projective, and CR structures are examples.

Tue 
Apr.29 
10:30  12:30 
Mike Eastwood (ANU) 
The Xray transform (part 1 and 2)
The simplest xray transform is a version of the Radon transform in three dimensions. One starts with a suitably decaying function of three variables and integrates it over the lines in Euclidean threespace obtaining a function on the fourdimensional space of lines. This transform is often named after John who identified its range in 1938. There are many variations on this theme! There is a compactified version, due to Funk in 1913. There is a complex version, due to Bateman in 1904. Nowadays, there are all sorts of xray transforms and the purpose of these lectures will be to describe the links between them and to use representation theory and differential geometry to establish their range and kernel in various cases. This is a repeat of talks given at the 34th Czech Winter School in Srni in January this year: they are aimed at a broad geometricallyinclined audience.

Thu 
May 1 
11:30  12:30 
Mike Eastwood (ANU) 
The Xray transform (part 3)

Tue 
May 20 
11:30  12:30 
Dennis The (ANU) 
Homogeneous integrable Lagrangean contact structures in dimension five 
Tue 
July 8 
11:30  12:30 
Simon Gindikin (Rutgers) 
The CauchyFantappie formula and the holomorphic language for
analytic cohomology
The CauchyFantappie integral formula has interesting possibilities for explicit computations of residues similar to
onedimensional classical receipts. I'll illustrate it on examples from analytic duality on symmetric spaces.

Mon 
July 28 
11:30  12:30 
Rupert MacCallum (University of Munster) 
TBA 
Wed 
Aug. 13 
11:30  12:30 
Mike Eastwood (ANU) 
Metrisability of threedimensional path geometries
Given a projective structure on a threedimensional manifold, we find some explicit obstructions to the local existence of a LeviCivita connection in the projective class (given as projectively
invariant tensors algebraically constructed from the projective Weyl curvature). As a separate issue, this raises some purely algebraic questions concerning classical invariant theory. There
will be examples. This is joint work with Maciej Dunajski.

Mon 
Nov. 17 
11:30  12:30 
Gerd Schmalz (University of New England) 
ChernMoser theory for paraCRmanifolds and degenerate multicontact structures
A 3dimensional nondegenerate paraCR manifold is nothing but the solution manifold of a second order ODE and its geometry has been thoroughly studied under different names and in various
contexts. I will present an approach analogous to ChernMoser normal forms for nondegenerate and degenerate paraCR manifolds. This is joint work with Alessandro Ottazzi (Trento).

Tue 
Nov. 18 
11:30  12:30 
Alexandr Medvedev (University of New England) 
Fundamental invariants of systems of ODEs of higher order
We find the complete set of fundamental invariants for systems of
ordinary differential equations of order >=4 under the group of point
transformations generalizing similar results for contact invariants of
a single ODE and point invariants of systems of the second and the
third order.
To obtain results we use theory of geometric structures on filtered
manifold and Cartan connections. This allows us to transfer main
difficulty to essentially algebraic computations of special Lie algebra
cohomologies associated with the problem.

Wed 
Nov. 26 
11:30  12:30 
David Ridout (ANU) 
Algebra vs Geometry: A showdown in physics
I'd like to pose a challenge to geometers (and/or topologists) relating to our current understanding of certain toy models for string theory called the WessZuminoWitten theories. In essence,
there are certain textbook cases that are well understood by using algebras and representations as well as by using geometry and topology. Recent work has clarified the algebraic structure of
many more cases. However, a geometric realisation of these cases is completely missing. I will introduce this story with the simplest example, when the string spacetime is a rank 1 Lie group.

Tue 
Dec. 2 
3:30  4:30 (LG15) 
Callum Sleigh (University of Auckland) 
Tractor calculus, BGG complexes, and cohomology of discrete groups.
Let M = \Gamma \ H^n be a compact, orientable, totally geodesic hyperbolic manifold. We will study M using the tools of
tractor calculus by viewing the hyperbolic structure as a holonomy reduction of a Cartan
geometry. In particular, if F is an irreducible SO(n,1)module, we give an isomorphism between the algebraic group
cohomology H(\Gamma, F) and the cohomology of an appropriate BGG complex on M. Moreover, these tools can be
used to prove a nonvanishing theorem for H^1(\Gamma, F) when M contains a compact, orientable, totally geodesic
hypersurface.
(Joint work with Rod Gover, University of Auckland)
