Jan Felipe van Diejen
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RECENT MEETINGS:* Algebraic methods in mathematical physics - Satellite event to the ICMP 2018 , July 16-20, 2018, Centre de recherches mathématiques, Montréal, Canada
* 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC) , July 16-20, 2018, Dartmouth college in Hanover, New Hampshire, USA
* VII Iberoamerican Workshop in Orthogonal Polynomials and Applications (EIBPOA2018) , July 3-6, 2018, Universidad Carlos III de Madrid (UC3M), Madrid, Spain
* SIDE 12 International Conference Symmetries and Integrability of Difference Equations, July 3-9, 2016, Sainte-Adèle, Canada
* KITP Conference: Non-equilibrium dynamics of stochastic and quantum integrable systems , February 16-19, 2016, Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California, USA
* BIRS workshop on Orthogonal and Multiple Orthogonal Polynomials , August 9-14, 2015, Oaxaca, Mexico
* XVIIIth International Congress on Mathematical Physics , July 27-August 1, 2015, Santiago, Chile
* Representation Theory, Special Functions and Painlevé Equations, March 3-6, 2015, RIMS, Kyoto University, Kyoto, Japan
* Foundations of Computational Mathematics FoCM’14 Workshop: Special functions and orthogonal polynomials , December 18-20, 2014, Montevideo, Uruguay
* Exact Solvability and Symmetry Avatars, Conference held on the occasion of Luc Vinet's 60th birthday, August 25-29, 2014, Centre de recherches mathématiques, Montréal, Canada
From Macdonald Processes to Hecke Algebras and Quantum Integrable Systems , May 26-30, 2014, Institut Henri Poincaré, Paris, France
My research concentrates on the Mathematics of
This is a branch of
Mathematical Physics that studies
Exactly Solvable Models and
Solitons, using tools from algebra, analysis and geometry….
I am particularly interested in one-dimensional (quantum) integrable particle systems like the Lieb-Liniger model, the Calogero-Moser-Sutherland system, and the Toda chain. Some of my main contributions deal with a class of (relativistic) deformations of these particle systems known as the Ruijsenaars-Schneider models, and with their connections to the Macdonald polynomials and the Macdonald-Koornwinder polynomials. Below is a list of some recent projects in which I have participated.
* Quadrature and cubature rules for random matrix ensembles
[2018a] van Diejen, J. F.; Emsiz, E.: Exact cubature rules for symmetric functions. Mathematics of Computation (2018).
[2018b] van Diejen, J. F.; Emsiz, E.: Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials. Proc. Amer. Math. Soc. 146 (2018), no. 12, 5333—5347.
* Discrete Fourier transform and generalizations
 van Diejen, J. F.; Emsiz, E.: Discrete Fourier transform associated with generalized Schur polynomials. Proc. Amer. Math. Soc. 146 (2018), no. 8, 3459–3472.
 van Diejen, J. F.; Emsiz, E.: A discrete Fourier transform associated with the affine Hecke algebra. Adv. in Appl. Math. 49 (2012), no. 1, 24–38.
* Difference equations for multivariate (confluent) hypergeometric functions
 van Diejen, J. F.; Emsiz, E.: Bispectral Dual Difference Equations for the Quantum Toda Chain with Boundary Perturbations. IMRN (2017).
 van Diejen, J. F.; Emsiz, E.: Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit. Adv. Math. 285 (2015), 1225–1240.
* Boundary perturbations for quantum integrable systems
 van Diejen, J. F.; Emsiz, E.; Zurrián, I. N.: Completeness of the Bethe Ansatz for an open q-boson system with integrable boundary interactions. Ann. Henri Poincaré 19 (2018), no. 5, 1349–1384.
 van Diejen, J. F.; Emsiz, E.: Integrable boundary interactions for Ruijsenaars' difference Toda chain. Comm. Math. Phys. 337 (2015), no. 1, 171–189.
 van Diejen, J. F.; Emsiz, E.: The semi-infinite q-boson system with boundary interaction. Lett. Math. Phys. 104 (2014), no. 1, 103–113.
* Macdonald polynomials
 van Diejen, J. F.; Emsiz, E.: Branching formula for Macdonald-Koornwinder polynomials. J. Algebra 444 (2015), 606–614.
 van Diejen, J. F.; Emsiz, E.: Orthogonality of Macdonald polynomials with unitary parameters. Math. Z. 276 (2014), no. 1-2, 517–542.
 van Diejen, J. F.; Emsiz, E. Unitary representations of affine Hecke algebras related to Macdonald spherical functions.: J. Algebra 354 (2012), 180–210.
[2011a] van Diejen, J. F.; Emsiz, E.: Pieri formulas for Macdonald's spherical functions and polynomials. Math. Z. 269 (2011), no. 1-2, 281–292.
[2011b] van Diejen, J. F.; Emsiz, E.: A generalized Macdonald operator. Int. Math. Res. Not. IMRN 2011, no. 15, 3560–3574.
* Spectral— and harmonic analysis of quantum integrable particle systems
 van Diejen, J. F.; Emsiz, E.: Orthogonality of Bethe ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove. Comm. Math. Phys. 350 (2017), no. 3, 1017–1067.
 van Diejen, J. F.; Emsiz, E.: Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term. Ann. Henri Poincaré 17 (2016), no. 7, 1615–1629.
 van Diejen, J. F.; Emsiz, E.: Diagonalization of the infinite q-boson system. J. Funct. Anal. 266 (2014), no. 9, 5801–5817.
 van Diejen, J. F.; Emsiz, E.: Discrete harmonic analysis on a Weyl alcove. J. Funct. Anal. 265 (2013), no. 9, 1981–2038.