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.
When I was still young and beautiful, I
worked on quantum probability theory, resulting in collaboration with
Luc Bouten and Jonas Kahn.
I then did my PhD in mathematics at Utrecht University. My supervisors were
Johan van de Leur,
Hans Maassen, and
After that, I was a postdoc at the universities of Hamburg (with
Christoph Schweigert), Erlangen-Nuernberg (with
Marius Crainic), and finally
Max Planck Institute in Bonn.
Apart from this,
some of my favourite collaborators are
Cornelia Vizman from Timisoara,
Leonid Ryvkin from Lyon,
my former colleague
my former postdoc
Tobias Diez (now Assistant Professor at the Shanghai Jiao Tong University),
my former PhD student
Lukas Miaskiwskyi, and my PhD student
- Local and multilinear noncommutative de Leeuw theorems (with Martijn Caspers, Amudhan Krishnaswami-Usha and Lukas Miaskiwskyi)
To appear in Mathematische Annalen, 2023.
- Positive energy representations of gauge groups I: Localization (with Karl-Hermann Neeb)
- Induced differential characters on nonlinear Grassmannians (with Tobias Diez, Karl-Hermann Neeb and Cornelia Vizman)
To appear in Annales de l'institut Fourier.
- The L-infinity algebra of a symplectic manifold (with Leonid Ryvkin and Cornelia Vizman)
Pacific Journal of Mathematics 314:1 (2021), 81-98.
- Central extensions of Lie groups preserving a differential form (with Tobias Diez, Karl-Hermann Neeb and Cornelia Vizman)
Int. Mat. Res. Notices 2021:5 (2021), 3794-3821.
- Pin Groups in General Relativity
Phys. Rev. D 101, 021702(R) (2020).
- Projective Unitary Representations of Infinite Dimensional Lie Groups (with Karl-Hermann Neeb)
Kyoto J. Math. 59:2 (2019), 293-341.
- Integrability of Central Extensions of the Poisson Lie Algebra via Prequantization (with Cornelia Vizman)
J. Symplectic Geom. 16:5 (2018), 1351-1375.
- Generalised Spin Structures in General Relativity
Ann. Henri Poincaré 19:5 (2018), 1587-1610.
Unifying Decoherence and the Heisenberg Principle
Lett. Math. Phys (2017) 107:1557-1579.
- Reflection Positive Doubles (with Arthur Jaffe)
J. Funct. Anal. 272, (2017), 3506-3557.
- 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.
- Covariant Central Extensions of Gauge Lie Algebras (with Karl-Hermann Neeb)
In: Albeverio S., Cruzeiro A., Holm D. (eds) Stochastic Geometric Mechanics, CIB-SGM 2015.
- Momentum Maps for Smooth Projective Unitary Representations (with Karl-Hermann Neeb)
In: Geometric Methods in Physics. XXXIV Workshop 2015. Trends in Mathematics 115-227.
- Central extensions of Lie algebras of symplectic and divergence free vector fields (with Cornelia Vizman)
Banach Center Publications 110 (2016), 105-114.
- 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)
J. 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).
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 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
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:
Seminar on Quantum Information Theory
Together with Martijn Caspers,
we are organising a seminar on quantum information theory.
08/11/2017 Probability spaces, Quantum probability spaces and von Neumann algebras
Finite dimensional systems, Bell games.
(First chapter of the
Lecture Notes of Hans Maassen.)
The quantum FFT algorithm and factorisation.
(Chapter II.5 of "Quantum computation and quantum information" by Nielsen and Chuang.)
Completely positive maps, dilations, graph capacities and the no cloning theorem.
(Chapter 4, 5 and 6 of the
Lecture Notes of Paulsen.)
Mathematics of on Quantum Information Theory
Together with Jop Briet, Martijn Caspers, and Maris Ozols, we organized a workshop on
`Mathematics of Quantum Information Theory' at the Lorenz center in Leiden.
For abstracts and slides of the talks, click here.
As you are behind a screen already, the easiest way to reach me is presumably by email:
mail "at" bjadres.nl