Bas Janssens

Welcome to my homepage. Currently, I am a postdoc at the Institute of Mathematics of the University of Utrecht, working in the Poisson Geometry Group of Marius Crainic. In January, I will move to the Max Planck Institute in Bonn.

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.


When I was still young and beautiful, I worked on quantum probability theory, resulting in collaboration with Hans Maassen, Madalin Guta, Luc Bouten and Jonas Kahn. I did my PhD in mathematics at Utrecht University, working on infinite dimensional Lie algebras. My supervisors were Johan van de Leur, Hans Maassen, and Roberto Fernández. After that, I was a postdoc with Christoph Schweigert at the University of Hamburg, where I collaborated closely with Christoph Wockel. I then went to the the Friedrich-Alexander University of Erlangen-Nuernberg, where I worked closely together with Karl-Hermann Neeb.


- Characterization of reflection positivity: Majoranas and spins (with Arthur Jaffe)
   Comm. Math. Phys. 346, (2016), 1021-1050.
- Universal central extension of the Lie algebra of Hamiltonian vector fields (with Cornelia Vizman)
   Int. Mat. Res. Notices 16:16 (2016), 4996-5047.
- Infinitesimally natural principal bundles
   J. Geom. Mech. 8:2 (2016), 199-220.
- Momentum Maps for Smooth Projective Unitary Representations (with Karl-Hermann Neeb)
  `Proceedings of the XXXIV Workshop on Geometric Methods in Physics', accepted 24-01-2016.
- Central extensions of Lie algebras of symplectic and divergence free vector fields (with Cornelia Vizman)
  `Proceedings of the Conference Geometry of Jets and Fields' (Banach center Publications), accepted 20-12-2015.
- Positive energy representations of gauge groups
   Oberwolfach Report 55/2014.
- Norm continuous unitary representations of Lie algebras of smooth sections (with Karl-Hermann Neeb)
   Int. Mat. Res. Notices 15:18 (2015), 9081-9137.
- Universal Central Extensions of Gauge Algebras and Groups (with Christoph Wockel)
   J. Reine angew. Math. 682 (2013), 129-139.
- Universal Central Extensions of Gauge Groups
   Oberwolfach Report 51/2010, 3023-3026.
- Optimal estimation of qubit states with continuous time measurements (with Madalin Guta and Jonas Kahn)
   Comm. Math. Phys. 277, (2008), 127-160.
- Characteristic function of the Heston-Hull-White model (with Fang Fang)
   Proceedings of the Fifty-Eighth European Study Group Mathematics with Industry (2007).
- Classical Coding and the Cauchy-Schwarz Inequality
   Quantum Stochastics and Information, Statistics, Filtering and Control (2006).
- Information Transfer Implies State Collapse (with Hans Maassen)
   Phys. A: Math. Gen. 39 (2006) 9845-9860.
- Optimal Pointers for Joint Measurement of sigma-x and sigma-z via Homodyne Detection (with Luc Bouten)
   J. Phys. A: Math. Gen. 39 (2006) 2773-2790.


- Transformation & Uncertainty. Some Thoughts on Quantum Probability Theory, Quantum Statistics, and Natural Bundles
   PhD Thesis (2010).
- Quantum Measurement, a coherent description
   Master's thesis (2004).


- Reflection Positive Doubles (with Arthur Jaffe)
- Covariant Central Extensions of Gauge Lie Algebras (with Karl-Hermann Neeb)
- Integrability of Central Extensions of the Poisson Lie Algebra via Prequantization (with Cornelia Vizman)
- Projective Unitary Representations of Infinite Dimensional Lie Groups (with Karl-Hermann Neeb)
- 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).

Work In Progress

At the moment, I'm working on the following papers. (Preprints of the first paper will appear on the arXiv before long.)

- 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


Here are some lecture notes and links for courses I taught in the past:

- 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.

Seminar on Lie Algebra Sheaves

In February 2014, Ori Yudilevich and I gave a 5-lecture seminar on Lie Algebra Sheaves, where we tried to understand, streamline and generalise the 1965 paper of Singer-Sternberg. Here are the notes for the talks I gave:

- Lecture2.pdf

- Lecture5.pdf

Contact information

As you are behind a screen already, the easiest way to reach me is presumably by email: mail "at"