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Homepage of Ralph L. Klaasse

Ralph Klaasse
Personal details.

I am a postdoctoral researcher in the geometry group of the Université libre de Bruxelles, working with Joel Fine. I obtained my Ph.D. from Utrecht University under supervision of Gil Cavalcanti, and was a member of the Geometric Structures group led by Marius Crainic.

Links to: arXiv preprints page, Google scholarResearchGate and LinkedIn.

Research interests.

My research interests consist mainly of Poisson geometry and generalized complex geometry, specifically the usage of Lie algebroids to extend symplectic techniques to this setting. Moreover, I am interested in surrounding areas such as symplectic geometry, Seiberg-Witten gauge theory, Dirac geometry, index theory, and low-dimensional topology. Recently, I am moreover interested in hypersymplectic geometry and the study of symplectic Lie groupoids.

Papers and preprints.
  1. Fibrations and log-symplectic structures, arXiv:1606.00156 (with Gil Cavalcanti), J. Symplectic Geom. 17 (2019), no. 3, 603-638. Available online.
  2. Fibrations and stable generalized complex structures, arXiv:1703.03798 (with Gil Cavalcanti), Proc. Lond. Math. Soc. 117 (2018), no. 6, 1242-1280. Available online.
  3. Classification of boundary Lefschetz fibrations over the disc, arXiv:1706.09207 (with Stefan Behrens, Gil Cavalcanti), Geometry and Physics: Volume 2, Chapter 15 (Oxford University Press, 2018). Available online.
  4. Poisson structures of divisor-type, arXiv:1811.04226. Submitted.
  5. Obstructions for symplectic Lie algebroids, arXiv:1811.05084. Submitted.
  6. Self-crossing stable generalized complex structures, arXiv:2004.07559 (with Gil Cavalcanti, Aldo Witte). Submitted.
Ph.D. thesis.
  • Geometric structures and Lie algebroids, arXiv:1712.09560. Utrecht University, 2017.
  • Constructing stable generalized complex four-manifolds, link.
    Notes for a talk at GQT School and Colloquium, June 2018.
In preparation.
Below is an incomplete list of papers that are currently in preparation.
  • Dirac and generalized complex structures of divisor-type.
  • Symplectic groupoids of elliptic Poisson structures (with Songhao Li).
  • Poisson cohomology of almost-regular Poisson manifolds (with Melinda Lanius).

Département de Mathématique
Université Libre de Bruxelles
CP 218, Boulevard du Triomphe
B-1050 Bruxelles, Belgique


Phone: +32 (0) 2 650 5837