17.10.25	Jakob Hedicke (Nijmegen) Positive paths of diffeomorphisms on manifolds with a contact structure Abstract: Given a (co-oriented) contact manifold, one can study paths of diffeomorphisms that are positively transverse to the contact distribution. For groups of contactomorphisms (diffeomorphisms preserving the contact structure) this leads to the well-studied notion of orderability. In this talk we study positive paths on the full group of diffeomorphisms. In particular we show that diffeomorphism groups are never orderable. As an application we answer a question about equilibrium Legendrian submanifolds in a thermodynamic phase space recently posed by Entov, Polterovich and Ryzhik.
7.11.25	Aldo Witte (Hamburg) bk-symplectic geometry from Lie algebroid deformations Abstract: bk-symplectic structures, as studied by Scott, Miranda and co-authors, are singular symplectic structures with poles of order k along an embedded hypersurface Z. These can be described as mildly degenerate Poisson structures, and are in part motivated by the description of the restricted three-body problem. A key ingredient in the description of these singular symplectic structures are the bk tangent bundles, which are Lie algebroids which capture the singularities of the symplectic form. Intuitively, these Lie algebroids are given by the vector fields which are ``tangent to order k'' to the hypersurface Z. However, for k ⩾ 2 this is not a well-defined notion: there are many Lie algebroids which can be said to consist of vector fields tangent to order k to Z. In joint work with Francis Bischoff and Álvaro del Pino we classified all these possible Lie algebroids. In this talk, I would like to introduce new singular symplectic structures on these Lie algebroids which display behaviour distinct from the existing bk-symplectic structures. These structures will arise by showing that under favourable conditions any deformation of the Lie algebroid will give rise to a deformation of bk-symplectic forms.
21.11.25	Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Bochum-Essen-Köln-Wuppertal) in Köln
9.1.26	Marcelo R. R. Alves (Augsburg) From curve shortening to Birkhoff sections of geodesic flows Abstract: In this talk, based on joint work with Marco Mazzucchelli, I will present some new results on the dynamics of geodesic flows of closed Riemannian surfaces, proved using the curve shortening flow. The first result is a forced existence theorem for orientable closed Riemannian surfaces of positive genus, asserting that the existence of a contractible simple closed geodesic γ forces the existence of infinitely many closed geodesics in every primitive free homotopy class of loops and intersecting γ. I will then explain how this type of result can be used to show the existence of Birkhoff sections for the geodesic flow of any closed orientable Riemannian surface.
16.1.26	Michael Wiemeler (Münster) Positive curvature and torus actions Abstract: In the 1930s Hopf asked whether every closed Riemannian manifold with positive sectional curvature and even dimension has positive Euler characteristic. In this talk I will discuss recent results that give an affirmative answer to this question under symmetry assumptions. The presented results are joint work with Lee Kennard and Burkhard Wilking.
23.1.26	Stéphanie Cupit-Foutou (Bochum) How to construct some non-Kähler compact complex manifolds Abstract: I will explain how to generalize the construction of an Hopf manifold as a quotient of a Lie group fibered over an orbifold to obtain new non-Kähler complex manifolds.
30.1.26	Fabio Gironella (Nantes) Vanishing cycles for symplectic foliations Abstract: Taut codimension 1 foliations are notoriously rigid in ambient dimension 3: as proved by Novikov in 1964, they give for instance non-trivial topological constraints on the ambient manifold. In higher ambient dimensions, this kind of foliations is on the other hand extremely flexible, and satisfies an h-principle. Strong symplectic foliations are a natural high-dimensional generalization of 3-dimensional taut foliations that instead behave much more rigidly, i.e. in a geometrically interesting way. One of the reasons for this rigidity is that symplectic techniques such as pseudo-holomorphic curves à la Gromov work well for strong symplectic foliations. I will present a joint work with Klaus Niederkrüger and Lauran Toussaint, where we give a new obstruction for a symplectic foliation to be strong. This comes in the form of a Lagrangian high-dimensional version of vanishing cycles for smooth codimension 1 foliations on 3-manifolds, which are known not to exist in the taut case due to a famous work of Novikov. The proof relies exactly on pseudo-holomorphic curve techniques, in a way which is parallel to the case of the Plastikstufe introduced by Niederkrüger in 2006 in the contact setting.

H. Geiges, 26.9.25