Welcome to my homepage. I am an assistant professor (UD) at the Institute of Applied Mathematics (DIAM) of Delft University of Technology (TU Delft).

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 am interested in String Geometry.

Preprint

- Positive energy representations of gauge groups I: Localization (with Karl-Hermann Neeb)

- How an action that stabilizes a bundle gerbe gives rise to a Lie group extension (with Peter Kristel)

Preprint

- Local and multilinear noncommutative de Leeuw theorems (with Martijn Caspers, Amudhan Krishnaswami-Usha and Lukas Miaskiwskyi)

- Induced differential characters on nonlinear Grassmannians (with Tobias Diez, Karl-Hermann Neeb and Cornelia Vizman)

To appear in

- The L-infinity algebra of a symplectic manifold (with Leonid Ryvkin and Cornelia Vizman)

- Central extensions of Lie groups preserving a differential form (with Tobias Diez, Karl-Hermann Neeb and Cornelia Vizman)

- Pin Groups in General Relativity

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

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

- Generalised Spin Structures in General Relativity

- Unifying Decoherence and the Heisenberg Principle

- Reflection Positive Doubles (with Arthur Jaffe)

- Characterization of reflection positivity: Majoranas and spins (with Arthur Jaffe)

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

- Infinitesimally natural principal bundles

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

In: Albeverio S., Cruzeiro A., Holm D. (eds)

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

In:

- 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).

- Positive Energy Representations of Gauge Groups II: Conformal Completion of Space-Time (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

- Introduction to Quantum Information and Computing (AM4645), TU Delft. Here are the lecture notes for 2023/2024.

- Differential Geometry (AM3580), TU Delft. Here are the lecture notes for 2023/2024.

- Analysis 2 (AM1070), TU Delft.

- 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

08/11/2017 Probability spaces, Quantum probability spaces and von Neumann algebras

15+22/11/2017 Finite dimensional systems, Bell games. (First chapter of the Lecture Notes of Hans Maassen.)

29/11/2017 The quantum FFT algorithm and factorisation. (Chapter II.5 of "Quantum computation and quantum information" by Nielsen and Chuang.)

6+13/12/2017 Completely positive maps, dilations, graph capacities and the no cloning theorem. (Chapter 4, 5 and 6 of the Lecture Notes of Paulsen.)