Oberseminar Geometrie, Topologie und Analysis

Oberseminar Geometrie, Topologie und Analysis

H. Geiges, I. Mărcuț, G. Marinescu, S. Sabatini, D. V. Vu

Wintersemester 2025/26

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

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)
b^k-symplectic geometry from Lie algebroid deformations

Abstract: b^k-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 b^k 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 b^k-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 b^k-symplectic forms.

21.11.25 Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Bochum-Essen-Köln-Wuppertal) in Köln

H. Geiges, 26.9.25


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) b^k-symplectic geometry from Lie algebroid deformations Abstract: b^k-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 b^k 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 b^k-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 b^k-symplectic forms.
21.11.25	Joint Seminar on Complex Algebraic Geometry and Complex Analysis (Bochum-Essen-Köln-Wuppertal) in Köln