Since April 2012 I am a postdoc at the Institut für Theoretische Physik of the Leibniz Universität Hannover, in the Quantum Information Group. I am supported by a NWO Rubicon grant. Before I was a PhD student of Michael Müger and Klaas Landsman, in the mathematical physics group at Radboud University Nijmegen. My PhD thesis can be found below.
Contact details
Pieter Naaijkens 
Leibniz Universität Hannover 
Institut für Theoretische Physik 
Appelstraße 2 
30167 Hannover 
Deutschland 
Email:  pieter.naaijkens AT ..hostname.. (please replace ..hostname.. by itp.unihannover.de) 
If you want to contact me by signed or encrypted mail: my GnuPG key ID is #B5A5E651.
Research
I am interested in the mathematical intricacies of topologically ordered systems. In particular, I try to use the tools and techniques of operator algebra, algebraic quantum field theory and tensor categories in this setting. For example, one can study the properties of the excitations of such systems by mimicking the DoplicherHaagRoberts theory of superselection sectors, a toolkit in algebraic quantum field theory, in the setting of topologically ordered spin systems. It turns out that this works very well: one can recover for example all excitations and their fusion rules and statistics for the toric code in this setting. This algebraic approach also appears to be very fruitful to study, e.g., the classification of topological phases
Publications
Articles and preprints
 LiebRobinson bounds, Arveson spectrum and HaagRuelle scattering theory for gapped quantum spin systems (with S. Bachmann and W. Dybalski), 2014 (preprint)
 Haag duality for Kitaev's quantum double model for abelian groups (with L. Fiedler), 2014 (preprint)
 Quantum spin systems on infinite lattices
Lecture notes for a onesemester course given at Leibniz Universität, 2013 (preprint)  KosakiLongo index and classification of charges in 2D quantum spin models
J. Math. Phys. 54:0819011–17, 2013 (journal  preprint)  Haag duality and the distal split property for cones in the toric code
Lett. Math. Phys. 101:341–354, 2012 (journal  preprint)  Localized endomorphisms in Kitaev's toric code on the plane
Rev. Math. Phys. 23:347–373, 2011 (journal  preprint)  On the extension of stringlike localised sectors in 2+1 dimensions
Comm. Math. Phys. 303:385–420, 2011 (journal  preprint)  Topologische kwantumcomputers: rekenen met vlechten
Nieuw Arch. Wiskd. 11:187–193, sept. 2010, semipopular, in Dutch (journal)  Fourpoint functions of differentweight operators in the AdS/CFT correspondence (with L. Berdichevsky)
JHEP 0801:071, 2008 (journal  preprint)
Theses
 Anyons in infinite quantum systems: QFT in d=2+1 and the toric code, PhD Thesis, Radboud University, 2012 (Defended May 15) (download)
 Fourpoint functions of N=4 SYM_{4} in the AdS/CFT correspondence, Master's Thesis, Utrecht University, 2007
 Cartesisch gesloten deelcategoriëen van Top, Bachelor's Thesis, Utrecht University, 2004
Please contact me if you would like a hardcopy version of my PhD thesis.
Talks
Here you can find a selection of my talks.
 TBA, AMS Joint Mathematics Meetings, MRC "Quantum" sessions (January 2015)
 The mathematics of topological quantum phases, Quantum information group seminar, Aachen (September 4, 2014)
 Superselection sectors in quantum spin systems (invited lecture), NSF/CBMS Conference on Quantum Spin Systems (June 13, 2014)
 Anyons as equivalence classes of representations of observables, BonnKölnAlgebra Seminar (October 29, 2013)
 Index and topological entanglement entropy, FU Berlin, Berlin (August 27, 2013)
 Elementary (quasi)particles with braided statistics, DPGFrühjahrstagung, Jena (February 28, 2013)
 Anyons in infinite quantum systems, Young Researcher Symposium, International Congress on Mathematical Physics, Aalborg (August 4, 2012)
 Anyons in infinite quantum systems, NTH Mathematics Colloquium, Braunschweig (May 24, 2012)
 Haag duality in the toric code, 28^{th} workshop on foundartions and constructive aspects of QFT, Göttingen (July 1, 2012)
 Localised endomorphisms in Kitaev's Z_{2} model on the plane, 27^{th} workshop on foundartions and constructive aspects of QFT, Leipzig (November 20, 2010)
 Topological quantum computation and tensor categories, PhD Colloquium, Utrecht (June 23, 2010)
 Topological quantum computers, modular categories and superselection sectors, Oberseminar C*Algebren, Münster (February 2, 2010)
 Extensions of stringlike localised sectors to the DHR field net, 25^{th} workshop on foundations and constructive aspects of QFT, Göttingen (January 15, 2010)
 Topological quantum computers and modular categories Mathematics staff colloquium, Nijmegen (May 27, 2009)
 Topological quantum computers and modular categories EIDMA Seminar, Eindhoven (May 20, 2009)
 Topological quantum computers: towards a rigorous description, Philips Mathematics Award, Groningen (April 15, 2009)
 Cartesian closed subcategories of Top, Seminar on quantization, noncommutative geometry and symmetry, Nijmegen (February 12, 2008)
 A nontrivial test of the AdS/CFT correspondence, Seminar on quantization, noncommutative geometry and symmetry, Nijmegen (January 22, 2008)
Teaching
I am currently a teaching assistant for a course on Lie algebras and their representations in physics. Before I have taught in the following courses:
 Summer 2014: teaching assistant LieAlgebren und ihre Darstellungen in der Physik
 Summer 2013: teaching Quantum Spin Systems on Infinite Lattices. Lecture notes can be found here.
 Fall 2012: teaching assistant Ergänzungen zur klassischen Physik
 Spring 2011: teaching assistant Symmetry Breaking
 Spring 2010: teaching assistant Inleiding Fourieranalyse
 Fall 2009: teaching assistant Topologie
 Spring 2009: teaching assistant bachelor course Introduction to partial differential equations
 Spring 2008: teaching assistant for Analysis I
In August 2008, I gave a summer course (see here for information for participants) for highschool students who do not have the right prerequisites for admission to the mathematics bachelor program.
I also participated in the SprintUp program summer 2008 till summer 2010.
Events
I will attend the following conferences and workshops:
 AMS Joint Mathematics Meetings (January 1013, 2015)
Past events
 35^{th} workshop on "Foundations and constructive aspects of QFT" (November 1415, 2014)
 AMS Mathematical Research Communities: Mathematics of Quantum Phases of Matter and Quantum Information (June 2430, 2014)
 NSF/CMBS Conference on Quantum Spin Systems (June 1620, 2014)
 DPGFrühjahrstagung 2014, Berlin (March 1721, 2014)
 XVII Conference on Quantum Information Processing (February 37, 2014)
 33^{rd} workshop on "Foundations and constructive aspects of QFT" (November 1416, 2013)
 BonnKölnAlgebra Seminar on topological phases (October 29, 2013)
 QMath 12 (September 1013, 2013)
 32^{nd} workshop on "Foundations and constructive aspects of QFT" (May 31June 1, 2013)
 Benasque symposium on Topological Quantum Information (February 1216, 2013)
 International congress on mathematical physics (August 311, 2012)
 Mathematical Aspects of Quantum Field Theory and Quantum Statistical Mechanics (July 30August 1, 2012)

30^{th} workshop on "Foundations and constructive aspects of QFT" (June 22/23, 2012)

Workshop Topological Quantum Computing (September 1216, 2011)
 28^{th} workshop on "Foundations and constructive aspects of QFT" (July 1 and 2, 2011)
 Seminar "Topics in operator algebra" (weekly, seminars finished)
 27^{th} workshop on "Foundations and constructive aspects of QFT" (November 19 and 20, 2010)
 Conference Quantum Groups (August 30September 3, 2010)
 26^{th} workshop on "Foundations and constructive aspects of QFT" (June 18 and 19, 2010)
 25^{th} workshop on "Foundations and constructive aspects of QFT" (January 15 and 16, 2010)
 International congress on mathematical physics (August 38, 2009)
 Algebraic Quantum Field Theory  The first 50 years (July 2931, 2009)
 Summer School on Operator Algebras and Applications (June 1519, 2009)
 Nederlands Mathematisch Congres 2009 (April 14 and 15, 2009)
 23^{nd} workshop on "Foundations and constructive aspects of QFT" (January 30 and 31, 2009)
 DIAMANT meets GQT workshop (October 2731, 2008)
 ESI Program on Operator Algebras and cQFT (September 819, 2008)
 Summer school "Aspects of operator algebras and applications" (July 2125, 2008)
 Fifth European Congress for Mathematicians (July 1418, 2008)
 Stieltjes week on noncommutative integration (June 913, 2008)
 22^{nd} workshop on "Foundations and constructive aspects of QFT" (June 6 and 7, 2008)
From September 2008 until June 2011, I organised the PhD colloquium in Nijmegen.
Links
Some interesting weblogs and websites:
 MathOverflow
 Terence Tao's "What's new"
 The ncategory cafe
 Scott Aaronson's blog
 Quantum Frontiers (Caltech QI group blog)
 LQP2