Fri 
Jan 25 
2:00  3:00 
Jan Slovak (Masaryk University) 
Schwachhoeffer's construction and its consequences
Schwachhoeffer's construction of all special holonomies of symplectic connections starts from the homogeneous models of
contact parabolic geometries. The talk will try to link this phenomenon to conformally Fedosov structures.

Tue 
Jan 29 
11:30  12:30 
Lashi Bandara (ANU) 
Square roots of perturbed subelliptic operators on Lie groups
Subelliptic operators can be defined on Lie groups through an
algebraic basis with an associated subLaplacian being a fundamental
object. Interesting "divergenceform" operators arise when perturbing
this subLaplacian with bounded, complex, measurable coefficients. We
solve the Kato square root problem for such operators on connected Lie
groups. In the general setting we deduce inhomogeneous estimates and
when the group is nilpotent, we prove stronger homogeneous estimates.
Furthermore, we prove Lipschitz stability of the estimates under small
perturbations of the coefficients. This is joint work with Tom ter Elst
(Auckland) and Alan McIntosh (ANU).

Tue 
Feb 5 
11:30  12:30 
Mat Langford (ANU) 
A proof of the Lawson Conjecture
In 1970, Lawson conjectured that any embedded minimal torus in the
threesphere is congruent to the `obvious' one: the Clifford torus,
$Cliff :=\{z\in S^3\subset R^4 : z_1^2+z_2^2=z_3^2+z_4^2=1/2\}$. This
conjecture was recently proved in the positive by Brendle. The proof I
will present is similar in spirit to Brendle's. It is motivated by a
geometric technique for parabolic equations known as noncollapsing.
This technique transfers to the elliptic minimal surface problem since
minimal surfaces are stationary solutions of the mean curvature flow.

WED 
Mar 13 
11:00  12:00 
Vladimir Matveev (Jena) 
ObataTanno equation and parallel objects for cone structures
One of two main steps in the proof of the classical LichnerowiczObata and ObataYano conjectures was to understand the existence of a solution of the socalled ObataTanno equations. These are
certain systems of geometric PDE that naturally and independently appeared in different branches of mathematics; I will start my talk with historical overview.
In the mathematical part of my talk I will show that these equations are closely related to the existence of parallel tensors on the cone over the manifold and use this observation to show that
the existence of a nontrivial solution on a closed manifold implies that this manifold is a sphere or a complex projective space with the standard metric. This part of my talk is based on the
joint results with A. Fedorova, V. Kiosak, P. Mounoud and S. Rosemann.
I will also discuss in what sense the equations are projectively and hprojectively invariant. This part of my talk is an ongoing project with R. Gover.

Wed 
Mar 20 
11:00  12:00 
Konrad Schoebel 
Separation of Variables and Moduli Spaces of Stable Curves
Integrable Killing tensors are used to classify orthogonal coordinates
in which the classical HamiltonJacobi equation can be solved by a
separation of variables. We explicitly describe the projective variety
of integrable Killing tensors on the 3sphere and relate its algebraic
geometric properties to the differential geometric properties of the
corresponding Killing tensors. This leads to an isomorphism between the
moduli space of separation coordinates on the nsphere and a well known
object in algebraic geometry: the moduli space of stable curves of genus
zero with n+2 marked points.

Wed 
Mar 27 
11:00  12:00 
David Calderbank (University of Bath) 
What is... a parabolic building?
TBA

Fri 
May 24 
13:30  14:30 
Igor Zelenko (Texas A&M) 
Wilczynski type invariants in the geometry of distributions
The geometry of vector distributions can be studied very often via the path geometry of distinguished integral curves called abnormal extremal trajectories. This approach was developed by Boris
Doubrov and myself mainly for the uniform treatment of distributions of any rank and arbitrary high corank regardless of their Tanaka symbol and the main applications are outside of the scope of
the parabolic geometries. However, even for the classical equivalence problem of rank 2 distributions (fields of planes) in R^5 the approach gives a new insight on the classical Cartan tensor
of such distributions. In this case the approach gives the passage from one G2geometry to other ones (via the natural double fibration) and the Cartan tensor can be interpreted as the
Wilczynski invariant of selfdual curves in projective spaces. In particular, this gives an alternative way of computing the Cartan tensor via the Hamiltonian formalism. In this talk I would
like to concentrate on this computational aspect. If the time will permit the case of rank 3 distributions in R^6 will be discussed in this line as well.

Tues 
May 28 
10:00  11:00 
Matthew Randall (ANU) 
Local obstructions to projective surfaces admitting skewsymmetric Ricci tensor
A projective surface is a 2dimensional manifold equipped with a projective structure i.e. a class of torsionfree affine that have the same geodesics as unparameterised curves. Given any
projective surface we can ask whether it admits a torsionfree affine connection (in its projective class) that has skewsymmetric Ricci tensor. This is equivalent to solving a particular
semilinear overdetermined partial differential equation. It turns out that there are local obstructions to solving the PDE in two dimensions. These obstructions are constructed out of local
invariants of the projective structure.

Wed 
May 29 
11:00  12:00 
Amitesh Datta (ANU) 
The Classification of Symplectic Toric Manifolds
A 2ndimensional symplectic toric manifold is a compact connected symplectic manifold equipped with an effective hamiltonian action of an ntorus and with a corresponding moment map. Delzant
proved that symplectic toric manifolds are classified by Delzant polytopes  convex polytopes in Euclidean space satisfying certain conditions. Delzant's theorem is important, in part, due to
the various connections that exist between toric geometry and other branches of mathematics. In this talk, we will briefly sketch some fundamentals of symplectic geometry such as the
MarsdenWeinsteinMeyer theorem and the AtiyahGuilleminSternberg theorem and explain how these results lead to a proof of Delzant's theorem.

Tue 
July 9 
12:00  13:00 
Travis Willse (ANU) 
Doubrov and Govorov's exceptional (2, 3, 5)distribution
In his so called Five Variables paper, Cartan solved the equivalence problem for (2, 3, 5)distributions. In particular, he claimed to classify up to local equivalence such distributions with
infinitesimal symmetry algebra of rank 6, and gave an ostensible quasinormal form for such distributions whose harmonic curvature satisfies a natural degenerancy condition, which in particular
implied that all distributions in this class have solvable symmetry algebra. A few months ago, Govorov and Doubrov upended this classification by constructing such a distribution with
nonsolvable symmetry algebra, and have apparently shown that it is the only distribution Cartan missed, at least that satisfies a transitivity condition. (This counterexample was nearly found by
Strazzullo in his 2008 thesis.) This distribution enjoys several unusual features. For one, unlike all of the distributions that satisfy Cartan's normal form, the conformal structure it induces
via Nurowski's construction is not almost Einstein. Despite this, one can still find (with some effort) an ambient metric for this conformal structure and with some computer assistance show that
its holonomy is equal to (split, real) G_2, hence furnishing examples of two uncommon phenomena.

Tue 
Oct 15 
TBA 
Mike Eastwood (ANU) 
TBA (in algebra/topology seminar)

Tue 
Oct 17 
TBA 
Pawel Nurowski (Warsaw) 
TBA  alumni talk on space mission design
