SFB Retreat 2020

Maria in der Aue, 31 August - 4 September 2020

31 August
14:00 - 15:00 Markus Reineke
Fano quiver moduli spaces
1 September
9:00 - 10:00 Jakob Hedicke
Positive paths of contactomorphisms and cone structures

Abstract: Chernov and Nemirovski showed that timelike curves in a globally hyperbolic Lorentzian
spacetime are related to positive Legendrian isotopies in the isotopy class of the fibres of a unit
cotangent bundle. Similar results hold for globally hyperbolic cone structures. After an introduction
about cone structures and their geodesics, we will show how one can naturally associate to a cone
structure a positive path of contactomorphisms on a spherical cotangent bundle. From this path one
can recover the cone structure and a flow of cone geodesics. On the other hand every positive path
in Cont(ST*M) determines a (possibly non-smooth) cone structure on R×M. If the path satisfies
certain convexity conditions the resulting cone structure is smooth and globally hyperbolic and
the path corresponds to a cone geodesic flow.
11:00 - 12:00 Isabelle Charton
Tall and monotone complexity one spaces of dimension six
2 September
9:00 - 10:00 Kai Zehmisch
The Riemann moduli space of nodal curves
11:00 - 12:00 Lucas Dahinden
Subriemannian billiards

Abstract: In subriemannian geometry we study Riemannian manifolds with movement restricted to
a bracket generating subbundle of the tangent bundle. In this setting we define a billiard reflection law
using control theoretic methods. The billiard trajectories admit a symplectic description:
they lift to characteristic flow lines at the boundary of a domain in the cotangent bundle.
We will elaborate the highly symmetric example of the Heisenberg group,
which reveals strong connections to magnetic billiards.
3 September
9:00 - 10:00 Nikhil Savale
Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases
11:00 - 12:00 David Bechara Senior
On the relation between asymptotic action and asymptotic winding number
4 September
9:00 - 10:00 Abror Pirnapasov
Mean action and the Calabi invariant
11:00 - 12:00 Peter Albers
Symplectically convex curves and an isoperimetric inequality

H. Geiges, 27.8.20