R. Cluckers, J. Gordon, I. Halupczok: Local integrability results in harmonic analysis on reductive groups in large positive characteristic, Ann. Sci. Ecole Norm. Sup., Vol. 47, No. 6, (2014).
R. Cluckers, Y. de Cornulier, N. Louvet, R. Tessera, A. Valette: The Howe-Moore property for real and p-adic groups, Math. Scand., Vol. 109, No. 2, 201--224
(2011) arXiv:1003.1484.
R. Cluckers, F. Loeser: Motivic integration in mixed characteristic with bounded
ramification: a summary, bookchapter in: "Motivic integration and its interactions
with model theory and non-archimedean geometry, Volume 1", Cambridge University
Press (2011) pdf here.
R. Cluckers, J. Nicaise and J. Sebag (Editors): Motivic integration and its interactions
with model theory and non-archimedean geometry, Volume 1, Cambridge University
Press (2011).
R. Cluckers, J. Nicaise and J. Sebag (Editors): Motivic integration and its interactions
with model theory and non-archimedean geometry Volume 2, Cambridge University
Press (2011).
R. Cluckers, T. Hales, F. Loeser: Transfer Principle for the Fundamental Lemma,
in ``On the Stabilization of the Trace Formula´´, edited by
L. Clozel, M. Harris, J.-P. Labesse, B.-C. Ngô, International Press of Boston, ISBN: 978-1-57146-227-5, (2011).
R.
Cluckers, F. Loeser: Ax-Kochen-Ersov Theorems for p-adic integrals and motivic integration,
in Geometric methods in algebra and number theory, Y. Tschinkel and F. Bogomolov (Eds.), 2005,
Proceedings of the Miami Conference 2003,
math.AG/0410223.
R.
Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11, 2002 math.LO/0311433.
R.
Cluckers: Cell decomposition and p-adic integration, Thesis
(locally) published in Leuven (2002) math.LO/0301023.
R.
Cluckers: Classification of semi-algebraic p-adic sets up to
semi-algebraic bijection, Journal für die reine und
angewandte Mathematik, 540, 105 -
114 (2001) math.LO/0311434.
S.-W. Shin, N. Templier: Sato-Tate theorem for families and low-lying zeros of automorphic L-functions, with appendix A by R. Kottwitz and Appendix B by R. Cluckers, J. Gordon and I. Halupczok, to appear in Inventiones Mathematicae,
arXiv:1208.1945.
R. Cluckers, D. J. Miller: Uniform bounds on the decay of families of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function, submitted, arXiv:1304.6102.
E. Hrushovski, B. Martin, S. Rideau: Definable equivalence relations and zeta functions of groups,
With an appendix "Rationality results for p-adic subanalytic equivalence relations" by R. Cluckers, submitted, arXiv:math/0701011.
Thesis:
I started my Ph.D. studies in 1999 in Leuven under supervision of Prof. Dr. J. Denef, finishing in 2002.
All chapters of the thesis are published separately.
Saskia Chambille, Kien Nguyen, and Alexander Lemmens: PhD students
Arne Smeets and Pablo Cubides: postdocs
Current projects:
One of my most ambitious projects is to solve
Igusa's 1974 conjecture on exponential sums. The conjecture describes p-adic
exponential sums, i.e., exponential sums modulo powers of p, uniform in
p.
For a general overview on motivic integration, see the slides on
motivic integration of the series of talks by F. Loeser at the 2005 Seattle algebraic geometry meeting.
Visits and honors:
During the spring term of 2014, I gave the Nachdiplom-Lectures at the ETH Zürich. I was a MSRI Research during part of the spring term 2014, Berkeley, California. I obtained an ERC Consolidator Grant with title "Motivic Mellin transforms and exponential sums through non-archimedean geometry" with ERC Grant Agreement nr. 615722 and acronym MOTMELSUM, 2014 - 2019.
The CNRS of France awarded me with a "prime d'excellence" in 2011.
Students of the KU Leuven nominated me for best teaching assistant in math. I was a Marie Curie Fellow at the ENS in Paris for two years from 2003 on. Further, outside of mathematics, I won a first prize on the Belgian, national contest "Axion Classics" for classical piano for adolescents in 1994.
I accompanied on the piano, in his debuting years 1992 - 1997,
Filip Jordens, who
is now a professional actor and singer. At that time, we performed Jacques Brel, and he still often
does. We were once guests in the studios of the national Belgian Radio 1 and
we were once the warming up program for Arno.