Welcome to my homepage. I'm a postdoc at the Institute of Mathematics of the University of Utrecht, working in the Poisson Geometry Group of Marius Crainic. I am fascinated by symmetry, and the surprisingly elegant way in which it pops up in (symplectic) geometry and quantum theory. On a technical level, this translates into a fairly broad spectrum of research interests in the field of mathematics: At the moment, my research centers around the cohomology and representation theory of infinite dimensional Lie algebras of geometrical nature, such as gauge algebras and various types of Lie algebras of vector fields. I am also working with Arthur Jaffe on reflection positivity for Majoranas and parafermions, and I was a member of the Research Network String Geometry, a group of people who are, like me, interested in String Geometry.

- Universal central extension of the Lie algebra of Hamiltonian vector fields (with Cornelia Vizman)

- Infinitesimally natural principal bundles

- Momentum Maps for Smooth Projective Unitary Representations (with Karl-Hermann Neeb)

- Central extensions of Lie algebras of symplectic and divergence free vector fields (with Cornelia Vizman)

- Positive energy representations of gauge groups

- Norm continuous unitary representations of Lie algebras of smooth sections (with Karl-Hermann Neeb)

- Universal Central Extensions of Gauge Algebras and Groups (with Christoph Wockel)

- Universal Central Extensions of Gauge Groups

- Optimal estimation of qubit states with continuous time measurements (with Madalin Guta and Jonas Kahn)

- Characteristic function of the Heston-Hull-White model (with Fang Fang)

- Classical Coding and the Cauchy-Schwarz Inequality

- Information Transfer Implies State Collapse (with Hans Maassen)

- Optimal Pointers for Joint Measurement of sigma-x and sigma-z via Homodyne Detection (with Luc Bouten)

PhD Thesis (2010).

- Quantum Measurement, a coherent description

Master's thesis (2004).

(2016).

- Covariant Central Extensions of Gauge Lie Algebras (with Karl-Hermann Neeb)

(2015).

- Integrability of Central Extensions of the Poisson Lie Algebra via Prequantization (with Cornelia Vizman)

(2015).

- Projective Unitary Representations of Infinite Dimensional Lie Groups (with Karl-Hermann Neeb)

(2015).

- Bundles with a lift of infinitesimal diffeomorphisms

This preprint is split in two parts for publication. The first part is accepted in J. Geom. Mech. under the name `Infinitesimally natural principal bundles'.

- Unifying Decoherence and the Heisenberg Principle

(2006, revised 2015).

- Positive Energy Representations of Gauge Groups (Table of contents) with Karl-Hermann Neeb

- CPR-algebras (Table of contents) with Arthur Jaffe

Below are some notes on further projects I am working on currently. Feel free to read them, but WATCH OUT! These are NOT preprints, but unfinished DRAFTS, and they may contain mistakes.

- Notes on Defects and String Groups

- Notes on Localisation of Lie Algebra Cohomology

- Notes on a Double Complex for the Poisson Lie Algebra

- I gave a minicourse for the Summer School on Geometry in Utrecht (15/08/2016 - 26/08/2016). The course notes on Loop Groups can be found here.

- In the Winter Term 2015/2016, I taught Mathematics 3 for Chemists, SK-BWIS3, in Utrecht. Course information and exercises can be found on the page Wiskunde 3 voor Scheikundigen. The course notes Wiskunde 3 (Dutch) can be found here.

- In the Winter Term 2014/2015, I taught Wat is Wiskunde in Utrecht.

- In the Summer Term 2012, I taught the proseminar `Groups and Platonic Solids' for students in Mathematics Education in Hamburg. The lecture notes Gruppen und platonische Körper (German) can be found here.

- In the Winter Term 2008/2009, I taught the seminar `Het Project' on entropy in Utrecht. The course notes Entropie (Dutch) can be found here.

- Lecture2.pdf

- Lecture5.pdf