The 12th DIFFERENTIAL GEOMETRY DAY
Wednesday the 18th of May 2016
Thomas Bruun Madsen
(Aarhus University, DK)
SU(3)-invariant special geometry: rigidity and deformations
I shall discuss invariant special geometry on simply-connected compact manifolds
with a cohomogeneity one action of SU(3). My main focus will be geometries
defined by a closed quaternionic 4-form.
This talk is based on joint work with Diego Conti and Simon Salamon.
(Uppsala University, SE)
On geometric foliations and center of mass in mathematical general relativity
The notion of center of mass is a very important and effective tool for describing
the overall dynamics of a physical system. While in Newton's theory of gravity
center of mass is straightforwardly defined via the mass density, the situation in
general relativity is much more complicated. In this talk we will describe how to
define the center of mass of asymptotically Euclidean and asymptotically hyperbolic
manifolds using foliations by constant mean curvature surfaces (as first proposed by
Huisken and Yau in 1996) and discuss the relation of this construction to
Hamiltonian formulation of general relativity. Then we will present a new approach
to defining the center of mass of asymptotically Euclidean initial data sets for the
Einstein equations which serve as models for isolated systems in general relativity.
This is joint work with Carla Cederbaum and Julien Cortier.
(Université Paris Est, Marne-la-Vallée, FR)
Surface theory in homogeneous 3-space
I will give an introduction to the differential geometry
of curves and surfaces in Thurston's homogeneous 3-manifolds
with a particular scope on the role of harmonic map in the theory
of constant mean curvature surfaces and minimal surfaces.
(Westfälisches Wilhelms-Universität Münster, DE)
Homogeneous Einstein metrics
We will discuss general structure results for compact and
non-compact homogeneous Einstein manifolds. In low dimensions
classification results can be deduced. In higher dimensions we will
address the major open problems.