27th of March, Banach Center, Sniadeckich 8, room 405
9:00 - 10:00
Matthew Randall: Local obstructions to projective surfaces admitting skew-symmetric Ricci tensorAbstract: A projective surface is a 2-dimensional manifold equipped with a projective structure i.e. a class of torsion-free affine connections that have the same geodesics as unparameterised curves. Given any projective surface we can ask whether it admits a torsion-free affine connection (in its projective class) that has skew-symmetric Ricci tensor. This is equivalent to solving a particular system of semi-linear overdetermined partial differential equations that generalises the projectively Ricci-flat condition. 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.
10:00 - 11:00
Thomas Mettler: Characterizing classical minimal surfaces via the entropy differentialAbstract: Every minimal surface in Euclidean 3-space arising from some holomorphic null immersion into C3 admits a four-dimensional space of non-trivial deformations. Using complex projective geometry we construct a holomorphic quadratic differential P on the surface that is invariant under this four-dimensional deformation space. We characterize several important model surfaces in terms of P – including Enneper's surface, the catenoid and the helicoid. Joint work with J. Bernstein.
11:00 - 11:30
Coffee break
11:30 - 12:30
Wojciech Kryński: Paraconformal connections and totally geodesic surfacesAbstract: I will describe geometries which generalise Einstein-Weyl structures on three dimensional manifolds and projective structures on a surface. I will also present relations to point geometry of ODEs, Poisson structures and geometry of webs.
12:30 - 14:00
Lunch break
14:00 - 15:00
Thomas Leistner: TBA