Research team
Expertise
1) Geometric structures in differential geometry such as symplectic structures, contact structures, Poisson structures and generalized complex structures. Moreover, the study of singular variants of these and their description using Lie algebroids. 2) Semi-toric geometry and its relation with generalized complex geometry. 3) Classification of Lie algebroids
Singularities in semitoric and Poisson geometry.
Abstract
Integrable systems are dynamical systems with sufficiently many conserved quantities. Semitoric systems are especially well-behaved, yet still flexible enough to show interesting phenomena. Semitoric geometry strongly interacts with Poisson geometry, which in turn is linked to Hamiltonian dynamics and many other areas in mathematics and physics. This project aims at making use of these connections and at establishing new ones. Consequently, we will prove results on the interface of these fields. We will strengthen the connection to theoretical physics by studying a form of symmetry for singular torus fibrations called T-duality, which we will apply to generalized complex geometry. Within geometry we will establish a new relation between singular and foliated geometric structures. We will compare the description of singular differential forms in algebraic and differential geometry, via Lie algebroids and log structures respectively. Explicitly our objectives are: (1) Study and classify semitoric manifolds with singular symplectic structures. (2) Extend T-duality to singular torus fibrations. (3) Transform singular geometric structures into foliated geometric structures. (4) Establish a dictionary between singular symplectic and algebraic log geometry. Finishing these projects will pave the way for interesting new interactions between these areas of research.Researcher(s)
- Promoter: Hohloch Sonja
- Fellow: Witte Aldo
Research team(s)
Project type(s)
- Research Project