Maarten van Pruijssen

Mailing address:
Radboud Universiteit Nijmegen
Department of Mathematics
P.O. Box 9010
6500 GL Nijmegen
Visiting address:
Huygensgebouw
Heyendaalseweg 135
6525 AJ NIJMEGEN
email: m"dot"vanpruijssen"at"math"dot"ru"dot"nl
phone: --
office: HG03.709

Welcome to my homepage. I am an assistant professor at the department of mathematics of the Radboud University in Nijmegen. My research interests include spherical varieties, representation theory of Lie groups, harmonic analysis, algebraic groups, branching rules, matrix-valued orthogonal polynomials.

Together with Erik Koelink, Stein Meereboer and Philip Schloesser, I have organized a workshop in Nijmegen from 8 to 12 June 2026:

Quantum Symmetric Pairs, Hecke Algebras, and Representations: Exploring Spherical Functions (QSPHERE 2026).

Together with Wadim Zudilin and Erik Koelink, I have organized a conference in Nijmegen from 1 to 3 May 2024:

Hypergeometric and Orthogonal Polynomials Event (HOPE in May).

Together with Erik Koelink, I have advised the PhD students Philip Schloesser and Stein Meereboer, who worked on the project "Vector-valued Orthogonal Polynomials and Multiplicity Free Induction: Deformations and Quantizations" (NWO-M2, 2022-26). Both Philip and Stein have successfully defended their dissertations on August 24, 2026:

Philip Schloesser: Vector-valued Macdonald polynomials and where to find them.
Stein Meereboer: On quantum symmetric pairs and their associated spherical functions.

Together with Jasper Stokman, Mikhail Isachenkov and Erik Koelink, I have organized a seminar on Harmonic Analysis on Quantum Groups and Hecke Algebras (2022/23, 2023/24).

May 6-9, 2024, I have taught a mini course on "Orthogonal polynomials and representation theory" in the Orthonet School in Logroño.

Publications and preprints

preprint

M. van Horssen and M. van Pruijssen, An elementary approach to non-symmetric shift operators and their q-analogs, 2026 (preprint).
M. van Horssen and M. van Pruijssen, Non-symmetric Jacobi polynomials of type BC1 as vector-valued polynomials Part 2: Shift operators, 2024 (preprint).
M. van Pruijssen, The branching rules for SL(n+1,C),GL(n,C)) revisited: a spherical approach and applications to orthogonal polynomials, 2018 (preprint).

Publications

M. van Pruijssen, Vector-valued Heckman-Opdam polynomials: a Steinberg variation, 2023 (preprint), accepted for publication in Selecta Math. (N.S.).
E. Depuydt and M. van Pruijssen, Multiplicity-free induction for the pairs (GL_2 × GL_2, diag(GL_2)) and (SL_3, GL_2) over finite fields, accepted for publication in J. Algebra Appl. (preprint)
M. van Pruijssen and P. Román, Matrix-valued classical pairs related to compact Gelfand pairs of rank one: families and shift operators, Results Math. 80 (2025), no. 7, Paper No. 211, 36 pp.
M. van Horssen and M. van Pruijssen, Non-symmetric Jacobi polynomials of type BC1 as vector-valued polynomials Part 1: spherical functions, Indag. Math. (N.S.) 36 (2025), no. 2, 593–608. (preprint).
M. van Pruijssen and G. Pezzini, On the extended weight monoid of a spherical homogeneous space and its applications to spherical functions, Represent. Theory 27(2023), 815–886. (preprint).
P. Crooks and M. van Pruijssen, An application of spherical geometry to hyperkähler slices, Canad. J. Math. 73(2021),no3,687 -- 716. (preprint).
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, Journal of Functional Analysis, 278(7), 2020, 108411. (preprint)
M. van Pruijssen, Spherical functions on spheres of rank two, Proceedings 50th Sophus Lie Seminar, Banach Center Publications, vol. 113. (Preprint).
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.

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

Seminar Sophus Lie, Universität Paderborn, September 19, 2024, Orthogonal polynomials related to root systems and spherical functions.
9ECM, Seville 2024 (MiniSymposium: Orthogonal Polynomials and Special Functions), Intermediate Jacobi Polynomials.
HOPE in MAY 2024, Radboud Universiteit Nijmegen, May 3, 2024, Shift operators for a class of intermediate Jacobi polynomials of type BC2.

Show older talks

Geometry Seminar, Radboud Universiteit Nijmegen, May 24, 2018, Inverting the branching rules in a multiplicity free setting.
Algebra and Geometry Seminar, University of Köln, May 8, 2018, Inverting the branching rules in a multiplicity free setting.
Algebra and Geometry Seminar, University of Newcastle, Feb. 13, 2018, Inverting the branching rules in a multiplicity free setting.
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

03.10.2026 Weekend van de Wetenschap, de wiskundekraam in het Huygensgebouw.
14.11.2026 Open Dag Wiskunde, Radboud Universiteit.
04.12.2023 Proefstuderen, workshop over construeerbaarheid.
06.03.2021 DESDA-Ouderdag, workshop over construeerbaarheid (online).
Frülings-Uni 2018, workshop Die Schönheit von Seifenblasen für Oberstufen-Schülerinnen. Literatur: H. van Lint und J. Breeman, Zeepvliezen, Epsilon, 2004.
Herbst-Uni 2016, workshop Graphen und Farben für Oberstufen-Schülerinnen. Literatur: M. Aigner, G. Ziegler, Das Buch der Beweise, Springer 2010.

Teaching

Nijmegen

Thesis supervision. Please contact me by email if you are interested in writing a bachelor or master thesis with me. I have a couple of projects available:

Ba: Gelfand triples, invariant measures, Bessel functions over finite fields,
Ma: Quantization of a certain spectral triple, Horospherical subalgebras, Real spherical representations.

I can also provide custom-made topics or variations on the topics above.

Regular teaching.

2026/27 Q1-3. Mathematics
2026/27 Q3-4. Maattheorie
2026/27 Q1-4. Portfolio

2025/26 Q1-3. Mathematics
2025/26 Q3-4. Maattheorie
2025/26 Q1-4. Portfolio

2024/25 Q1-2. Mathematics
2024/25 Q1. Vector Calculus
2024/25 Q3-4. Sabbatical

Show older teaching duties

2023/24 Q1-3. Mathematics
2023/24 Q1. Vector Calculus
2023/24 Q3-4. Calculus B

2022/23 Q1-3. Mathematics
2022/23 Q1-2. Calculus A
2022/23 Q4. Linear Algebra for Science students

2021/22 Q4. Vector Calculus
2021/22 Q2-3. Ringen en Lichamen
2021/22 Q1-2. Seminar on Coxeter Groups
2021/22 Q1-3. Mathematics
2021/22 Q1-2. Calculus A
2021/21 Q1. Linear Algebra for Science students

2020/21 Q4. Vector Calculus
2020/21 Q2-3. Ringen en Lichamen/li>
2020/21 Q1-3. Mathematics
2020/21 Q1-2. Calculus A
2020/21 Q1. Linear Algebra for Science students

2019/20 Q4. Lineaire Algebra B
2019/20 Q4. Vector Calculus
2019/20 Q1-3. Mathematics
2019/20 Q1-2. Calculus A
2019/20 Q1-2. Master seminar

PADERBORN (Lehre auf deutsch).

Sommersemester 2018. Mannigfaltigkeiten, Teacher
Sommersemester 2018. WiWi, Übungsgruppe.
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.