Berlin-Hamburg-Hannover-Seminar am 23.01.2026

Felix Schlenk (Neuchatel) Markov numbers and symplectic embeddings

Markov numbers are triples (a,b,c) of natural numbers that solve the Markov equation a^2+b^2+c^2 = 3abc. While these triples parametrize classes of irrational numbers that can be approximated only very badly by rational numbers, they recently have played an important role for understanding certain symplectic embeddings. For instance, a Lagrangian p-pinwheel only embeds into the projective plane if p belongs to a Markov number, and the Fibonacci staircase describing the problem of symplectically embedding a four-dimensional ellipsoid into a four-ball of minimal size is just the case p=1 of a symplectic embedding problem associated to symplectic neighbourhoods of certain cyclic quotient singularities. I will try to explain these things and their relations in a non-technical way. This is based on joint work with Nikolas Adaloglou, Joé Brendel, Jonny Evans, and Johannes Hauber.

Georgios Dimitroglou-Rizell (Uppsala) Symplectic tools for fillability and non-fillability of certain rationally convex surfaces

Any totally real submanifold of the complex vector space is rationally convex (this is a notion from analytic function theory) if and only if it is isotropic (a symplectic notion) for some Kähler form, due to a classical result by Duval-Sibony. We use techniques from symplectic topology to show fillability by an embedded solid torus foliated by holomorphic discs when the surface is contained inside a pseudoconvex three-sphere by applying techniques from contact and symplectic topology. We also use symplectic and contact tools to provide examples of constructions of fillable and non-fillable rationally convex surfaces with only hyperbolic complex tangencies. This is joint work with Mark Lawrence.