Pieter Naaijkens' homepage

NOTE: This page is not up-to-date any more, and will not be updated in the future. Please consult my new homepage.

I work as a PhD student of Michael Müger and Klaas Landsman, in the mathematical physics group.

Contact details

You can visit me at:

Research

My current research interests are in local quantum physics and in category theory. In particular, I work on how structures arising in aQFT can be described categorically. My research focusses on connections with topological quantum computing. In particular, I am interested in rigorous treatment, using operator algebraic methods, of quantum spin models on an infinite lattice, from a local quantum physics viewpoint. In certain cases the superselection structure of such models can be described by braided tensor categories.

Publications

Articles and preprints

1. Haag duality and the distal split property for cones in the toric code, 2011 (preprint)
2. Localized endomorphisms in Kitaev's toric code on the plane
   Rev. Math. Phys. 23:347–373, 2011 (journal | preprint)
3. On the extension of stringlike localised sectors in 2+1 dimensions
   Comm. Math. Phys. 303:385–420, 2011 (journal | preprint)
4. Topologische kwantumcomputers: rekenen met vlechten
   Nieuw Arch. Wiskd. 11:187–193, sept. 2010, semi-popular, in Dutch (journal)
5. Four-point functions of different-weight operators in the AdS/CFT correspondence (with L. Berdichevsky)
   JHEP 0801:071, 2008 (journal | preprint)

Theses

1. Four-point functions of N=4 SYM₄ in the AdS/CFT correspondence, Master's Thesis, Utrecht University, 2007
   
2. Cartesisch gesloten deelcategoriëen van Top, Bachelor's Thesis, Utrecht University, 2004

Talks

Here you can find a selection of my talks.

• Localised endomorphisms in Kitaev's Z₂ 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)
• Cartesion closed subcategories of Top, Seminar on quantization, non-commutative geometry and symmetry, Nijmegen (February 12, 2008)
• A non-trivial test of the AdS/CFT correspondence, Seminar on quantization, non-commutative geometry and symmetry, Nijmegen (January 22, 2008)

Teaching

I have taught in the following courses:

• 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 high-school students who do not have the right prerequisites for admission to the mathematics bachelor program.

I also participated in the Sprint-Up program summer 2008 till summer 2010.

Events

Starting September 2008, I am organising the PhD colloquium.

• 28^th workshop on "Foundations and constructive aspects of QFT" (July 1 and 2, 2011)
• Seminar "Topics in mathematical physics"
• Algemeen wiskunde colloquium (weekly)
• Seminar on Quantization, non-commutative geometry and symmetry (regularly)

Past events

• 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 30-September 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 3-8, 2009)
• Algebraic Quantum Field Theory - The first 50 years (July 29-31, 2009)
• Summer School on Operator Algebras and Applications (June 15-19, 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 27-31, 2008)
• ESI Program on Operator Algebras and cQFT (September 8-19, 2008)
• Summer school "Aspects of operator algebras and applications" (July 21-25, 2008)
• Fifth European Congress for Mathematicians (July 14-18, 2008)
• Stieltjes week on noncommutative integration (June 9-13, 2008)
• 22^nd workshop on "Foundations and constructive aspects of QFT" (June 6 and 7, 2008)

Links

Some interesting weblog and websites:

• MathOverflow
• Wiskundemeisjes
• Terence Tao's "What's new"
• The n-category cafe