Yorkshire and Durham |
 |
Geometry Day at Leeds |
Yorkshire and Durham |
|
Geometry Day at Leeds |
Abstract (Bielawski): We shall discuss the asymptotic behaviour of Kaehler potentials and moment maps on Ricci-flat manifolds under different curvature assumptions. Applications to the geometry and topology of such manifolds and their Kaehler quotients will be given.
Abstract (Butler): This talk will review some results on the topology of a manifold which is the configuration space of an integrable mechanical system. A refinement of these results will be presented: the smooth structure of the configuration space is a non-trivial obstruction to the existence of an integrable mechanical system.
Abstract (Cabezas-Rivas): We will describe how we exploit the theory of Optimal Transport as a source of geometric intuition to build up the notion of Canonical Soliton. In particular, given a Ricci flow on a manifold M over a time interval I, we imagine the time parameter as an additional space direction and construct gradient Ricci solitons on the space-time M x I.
As an application, we shall see how our construction encodes various of the monotonic quantities that underpin Perelman's work on Ricci Flow, and how old and new Harnack inequalities naturally arise as simple curvature conditions on the space-time solitons.
Abstract (Kedra):
Based on ideas of Sternberg, Weinstein invented a notion of a fat bundle
in order to construct new examples of symplectic manifolds. This was in
the late 1970's.
In my talk I am going to
* show that many constructions of symplectic manifolds (e.g. certain
twistor bundles) are in fact via fat budles
* construct infinite dimensional examples
* apply fat bundles to the topology of the classifying space of the group
of Hamiltonian diffeomorphisms of a symplectic manifold
* apply fat bundles to cohomology of lattices in semisimple Lie groups