Hendrik De Bie

I teach the following courses at Ghent University:

• Mathematical Analysis 2 (1st bachelor engineering, ca. 400 students)

• Mathematical Analysis 3 (2nd bachelor engineering, ca. 300 students)

• Mathematical Analysis (2nd bachelor engineering: architecture, ca. 100 students)

• Function Spaces (3rd bachelor of mathematics, ca. 25 students)

Some current research topics include:

• Integrable systems of Dirac type

• Askey-Wilson, Bannai-Ito and Racah algebras

• Orthogonal polynomials and special functions in harmonic analysis

• Dunkl operators

• Generalized Fourier transforms in harmonic analysis

• EOS project: Partners in Research on Integrable Models and Applications
  
  

I have completed the supervision of more than 15 PhD students (see here for the genealogy) and I am currently supervising 2 PhD students.

Most of my publications can be found on this arxiv link. Ghent University also has an institutional repository, where all my published papers can be found.

I also have a google scholar profile. Citations to papers of mathematicians are usually low compared to other sciences, and are not a good quality indicator. The website mathcitations.github.io lists the highest cited mathematicians worldwide per graduation year, based on citation data of October 2018 from Mathscinet (the official database of the American Mathematical Society).

Here are some of my most important papers. Note that authors in mathematics are listed in alphabetical order. The American Mathematical Society has issued a professional statement about this, which you can consult here.

• H. De Bie, P. Lian, The Dunkl kernel and intertwining operator for dihedral groups. J. Funct. Anal. 280, 108932 (2021)

• H. De Bie, H. De Clercq, W. van de Vijver, The higher rank q-deformed Bannai-Ito and Askey-Wilson algebra. Comm. Math. Phys. 374, 277-316 (2020).

• H. De Bie, V. X. Genest, W. van de Vijver, L. Vinet,  A higher rank Racah algebra and the Z_2^n Laplace-Dunkl operator. J. Phys. A: Math. Theor. 51 (2018) 025203 (20pp).

• H. De Bie, D. Eelbode, M. Roels, The harmonic transvector algebra. J. Algebra 473 (2017), 247-282.

• H. De Bie, V. Genest and L. Vinet, The (Z_2)^n Dirac-Dunkl operator and a higher rank Bannai-Ito algebra. Adv. Math. 303 (2016) 390-414.

• H. De Bie, F. Sommen, M. Wutzig, Reproducing kernels for polynomial null-solutions of Dirac operators. Constr. Approx. 44 (2016), 339-383.

• H. De Bie, V. X. Genest, L. Vinet, A Dirac-Dunkl equation on S^2 and the Bannai-Ito algebra. Comm. Math. Phys. 344 (2016), 447-464.

• H. De Bie, R. Oste and J. Van der Jeugt, Generalized Fourier transforms arising from the enveloping algebras of sl(2) and osp(1|2). Int. Math. Res. Not. IMRN 2016 (15), 4649-4705.

• H. De Bie, B. Orsted, P. Somberg and V. Soucek, Dunkl operators and a family of realizations of osp(1|2). Trans. Amer. Math. Soc. 364 (2012), 3875-3902.

• H. De Bie and Y. Xu, On the Clifford-Fourier transform, Int. Math. Res. Not. IMRN 2011, no. 22, 5123-5163.

• K. Coulembier, H. De Bie and F. Sommen, Orthogonality of the Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. 103 (2011), 786-825.

• H. De Bie and F. Sommen, Spherical harmonics and integration in superspace, J. Phys. A: Math. Theor. 40 (2007), 7193-7212.

I am president of the Faculty Doctoral Committee of the Faculty of Engineering and Architecture.

Previously I was Head of the Department of Mathematical Analysis, which I successfully merged with the Department of Electronics and Information Systems.

I completed 2 Master degrees and graduated both with greatest distinction:

• Master in engineering physics (2000-2005)

• Master in pure mathematics (2001-2005)

I then obtained a PhD in Mathematics in 2008 supported through a research fellowship of the Research Foundation - Flanders (FWO - Vlaanderen). (2005-2008)

I subsequently was a Postdoctoral Fellow of the Research Foundation - Flanders (FWO), which included a 6 month stay at University of Oregon (visiting Yuan Xu) and a 6 month stay at University of Amsterdam (visiting Jasper Stokman and Eric Opdam). (2009-2011)

Subsequently:

• 2011-2016: Assistant Professor, Ghent University.

• 2016-2018: Associate Professor, Ghent University.

• 2018-now: Full Professor, Ghent University.