Maarten van Pruijssen

Mailing address:
Universität Paderborn
Institut für Mathematik
Warburger Str. 100
D-33098 Paderborn
email: vanpruijssen 'at' math.uni-paderborn.de
phone: (+49) 5251 - 60-2637
office: D 2.237
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Welcome to my homepage. In February 2013 I became post-doc in the research group of Bernhard Krötz at the Universität Paderborn. Prior to this I was a Ph.D. student under the supervision of Erik Koelink and Gert Heckman and co-supervision of Pablo Román.


Research interests

My research interests include (real) spherical varieties, representation theory of Lie groups, harmonic analysis, algebraic groups, branching rules, systems of matrix valued hypergeometric functions and matrix valued orthogonal polynomials.


Publications and preprints

preprint

  • M. van Pruijssen, Spherical functions on spheres of rank two, 2017, (preprint), submitted. See also the supporting software below.
  • E. Koelink and M. van Pruijssen and P. Román, Matrix elements of irreducible representations of SU(n+1) x SU(n+1) and matrix-valued orthogonal polynomials, 2017 (preprint), submitted.
  • M. van Pruijssen, The branching rules for (SL(n+1,C),GL(n,C)) revisited: a novel proof and applications, 2017 (preprint), submitted.
  • M. van Pruijssen and P. Román, Deformation of matrix-valued orthogonal polynomials related to Gelfand pairs, 2016 (preprint).
  • Publications

  • M. van Pruijssen, Multiplicity free induced representations and orthogonal polynomials, IMRN 2017(doi: 10.1093/imrn/rnw295) (preprint)
  • M. van Pruijssen and P. Román, Matrix valued classical pairs related to compact Gelfand pairs of rank one, SIGMA 10 (2014), 113, 28 pages (article).
  • G. Heckman and M. van Pruijssen, Matrix valued orthogonal polynomials for Gelfand pairs of rank one, Tohoku Math. J. (2) 68 (2016), no. 3, 407–437. (preprint).
  • E. Koelink and M. van Pruijssen and P. Román, Matrix valued orthogonal polynomials related to (SU(2)xSU(2), diag), II, Publ. RIMS Kyoto 49, no. 2, (2013), 271-312 (preprint).
  • E. Koelink and M. van Pruijssen and P. Román, Matrix valued orthogonal polynomials related to (SU(2)xSU(2), diag), International Mathematics Research Notices 2012, no. 24, 5673-5730 (preprint).

  • Software

    Together with Pablo Román I have written a GAP-code (Sp.g, SPn_lib.g) to calculate spherical functions on the compact Gelfand pair (Sp(2n),Sp(2n-2)xSp(2)). Feel free to improve and/or extend to other Gelfand pairs!

    The WHK/SHK-project: Representation theory, Computer Algebra and Special Functions that was kindly granted by the University of Paderborn resulted into two GAP-codes (PHI0.g, PHI0_library.g). These files came about with the help of my WHK (scientific assistant) Stanislav Smirnov. The results have been incorporated in the preprint Spherical functions on spheres of rank two. Here is a Mathematica notebook with a couple more calculations.


    In preparation

  • Extended weight semi-groups for multiplicity free systems, with Guido Pezzini.

  • Theses

  • Matrix valued orthogonal polynomials related to compact Gel'fand pairs of rank one, Ph.D.-thesis, 2012.
  • Tautological cycles on Jacobian varieties, master thesis, 2008.

  • Talks

  • Analysis Seminar, University of Glasgow, Mar. 28, 2017, Harmonic analysis on vector bundles.
  • Workshop on spherical varieties, Tsinghua Sanya International Mathematics Forum, Nov. 7, 2016, The classification of multiplicity free systems.
  • Seminar Sophus Lie, Bedlewo (Poland), Sept. 27, 2016, Vector-valued orthogonal polynomials in several variables.
  • Dunkl operators, special functions and harmonic analysis (Conference on the occasion of Charles Dunkl's 75th birthday), Paderborn, Aug. 8, 2016, Vector-valued orthogonal polynomials in several variables.
  • Emmy Noether Seminar, Erlangen, Jan. 15, 2016, Multiplicity free induction and orthogonal polynomials.
  • GQT Colloquium, Zandvoort aan Zee, Nov. 6, 2014, Multiplicity free induction and orthogonal polynomials.
  • DMV-PTM Meeting, Poznan, Sept. 2014, Multiplicity free induction and orthogonal polynomials.
  • Informal seminar, University of Tokyo, Sep. 4, 2013, Reductive spherical pairs and orthogonal polynomials.
  • JSPS-NWO Seminar Analysis, Geometry and Group Representations for Homogeneous Spaces, University of Nagoya, Aug 30, 2013, Reductive spherical pairs and orthogonal polynomials.
  • Conference `Representations of Lie Groups and Supergroups' , MFO Oberwolfach, Mar. 14, 2013, Spherical functions on compact Gel'fand pairs of rank one (slides).
  • Thesis defense, Laymen's talk, Radboud Universiteit Nijmegen, Dec. 19, 2012, Een geschiedenis.
  • Workshop `Special Functions and Lie Theory', Radboud Universiteit Nijmegen, Dec. 18, 2012, Spherical functions on compact Gel'fand pairs of rank one.
  • LMNRS Days, Université de Lorraine, Nancy, Nov. 30, 2012, Spherical functions on compact Gel'fand pairs of rank one.
  • DYGEST workshop on Integrable Systems, KU Leuven, Nov. 15, 2012, Matrix valued classical pairs from group theory.
  • Oberseminar "Darstellungs-Theorie", Universität Paderborn, Oct. 31, 2012, How compact Gel'fand pairs of rank one give rise to families of matrix valued orthogonal polynomials..
  • Seminario de Teoría de Lie, FaMAF - Universidad Nacional de Córdoba, Aug. 30, 2012, Matrix valued orthogonal polynomials related to compact Gelfand pairs of rank one.
  • Workshop on special functions, Radboud Universiteit Nijmegen, Jun. 16, 2012, Vector valued polynomials associated to multiplicity free triples.
  • Séminaire Analyse, Géométrie et Algèbre, Université de Lorraine, Laboratoire de Mathématiques et Applications de Metz, May 11, 2012, Vector valued polynomials associated to multiplicity free triples.
  • Intercity number theory seminar, CWI, Amsterdam, Mar 16, 2012, Multiplicity free systems.
  • 11th International symposium on orthogonal polynomials, special functions and applications, Universidad Carlos III de Madrid, Sep. 2, 2011, Matrix valued orthogonal polynomials related to a compact symmetric pair of rank one.
  • Ph.D.-colloquium, Radboud Universiteit Nijmegen, Dec. 2, 2010, Spherical Functions and MVOP's associated to the pair (SU(2)xSU(2),diag).
  • Seminar classical analysis, KU Leuven, Aug. 4, 2010, Matrix valued orthogonal polynomials associated to the pair (SU(2)xSU(2),diag).
  • AIO-colloquium, Universiteit Utrecht, Nov. 29, 2010, Spherical functions associated to the pair (SU(2)xSU(2),diag).
  • Ph.D.-colloquium, Radboud Universiteit Nijmegen, Nov. 20, 2008, Bolfuncties.

  • Outreach

  • Herbst-Uni 2016, Vorlesung Graphen und Farben für Oberstufen-Schülerinnen. Literatur: M. Aigner, G. Ziegler, Das Buch der Beweise, Springer 2010.

  • Seminars

    I am/have been an active participant in the local seminars on spherical varieties (which I organized in the SS2015 ), Lie theorie, Micro-local analysis, Algebraic analysis.

    During my Ph.D. I have been involved (participating and organizing) in several Ph.D.-seminars: Harmonic analysis, K-theory, Hilbert C*-modules, Geometry of schemes, Quantum groups, Morse theory.


    Teaching

    PADERBORN (Lehre auf deutsch). See the web page for course related stuff.

  • Sommersemester 2017. Darstellungstheorie, Teacher.
  • Sommersemester 2017. Seminar (Analysis und Geometrie), Teacher.
  • Wintersemester 2016/17. Mathe für Physiker C, TA.
  • Wintersemester 2016/17. Geometrie, TA.
  • Sommersemester 2016. Coxeter groups, Teacher (reading course).
  • Wintersemester 2015/16. Funktionalanalysis I, TA.
  • Wintersemester 2015/16. Lie groups, Teacher.
  • Sommersemester 2015. Proseminar Projektive Geometrie, Teacher.
  • Sommersemester 2015. Geometrie, TA.
  • Wintersemester 2014/15. Lineare Algebra 1, TA.
  • Sommersemester 2014. Lineare Algerba 2, TA.
  • Wintersemester 2013/14. Funktionalanalysis, TA.
  • Wintersemester 2013/14. Lineare Algebra 1, Übungsgruppe.
  • Sommersemester 2013. Lineare Algebra 2, TA.
  • NIJMEGEN (Teaching in Dutch or English).

  • Fall 2011, second half of the semester. Dynamische systemen, first year course using "An Introduction to Chaotic Dynamical Systems" by R. L. Devaney, Teacher.
  • Spring 2011, student seminar on reductive groups after "Linear Algebraic Groups, second edition" by T.A. Springer (see the web page), Teacher.
  • Fall 2010. Analysis II, second year analysis course using "Analysis II, second edition" by T. Tao, TA.
  • Spring 2010, second half of the semester. Complex Analysis, TA.
  • Summer 2009. Deficiency course for high school students, Teacher.
  • Fall 2009. Analysis II, second year analysis course using "Analysis II, second edition" by T. Tao, TA.
  • Spring 2009, first half of the semester. Kepler Laws (for freshmen), TA.
  • Fall 2008. Kepler Laws (for high school students), TA.
  • Fall 2008. Master course/seminar on hypergeometric functions, TA.
  • UTRECHT (Onderwijs in het nederlands).

  • < 2008. Various exercise classes for analysis and algebra, TA.

  • Bees

    Since 2015 my wife and I keep bees, we have a couple of hives in the orchard of our neighbor. On May 25 2017 one of the hives swarmed, but we were able to catch the swarm.