Directeur de Recherche du CNRS, France.
Associate professor (part time, 20%) at KU Leuven, Belgium.
ERC Consolidator Grant nr. 615722, MOTMELSUM, 2014 - 2019.
Université Lille 1 Sciences et Technologies
Laboratoire Painlevé, CNRS - UMR 8524
59655 Villeneuve d'Ascq Cedex (France)
Bureau: 314, building: M2
TEL: +33 320434193 and +32 16327025
3001 Leuven (Belgium)
Current and past Postdocs and PhD students:
Saskia Chambille, Kien Nguyen, and Alexander Lemmens: current PhD students.
Tristan Kuijpers and Eva Leenknegt: past PhD students.
Dmitry Sustretov, Jorge Cely, Wouter Castryck, Eva Leenknegt: current postdocs.
Pablo Cubides and Arne Smeets: past postdocs.
Published papers and books*:
Preprints and notes:
R. Cluckers, L. Lipshitz: Strictly Convergent Analytic Structures, J. Eur.
Math. Soc. (JEMS), Vol. 19, no. 1, 107 -- 149 (2017).
R. Cluckers, W. Veys: Bounds for
p-adic exponential sums and log-canonical thresholds, Amer. J. Math., Vol. 138, No. 1, 61 -- 80 (2016).
R. Cluckers, J. Gordon, I. Halupczok: Transfer principles for Bounds of motivic exponential functions, chapter in Families of automorphic forms and the trace formula,
Müller, Werner, Shin, Sug Woo, Templier, Nicolas (Eds.) ISSN
2365-9564, Springer (2016).
R. Cluckers, F. Martin: A definable, p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps, Journal of the Institute of Mathematics of Jussieu,
doi:10.1017/S1474748015000390, 1--19, (2015), © Cambridge University Press 2015.
R. Cluckers, G. Comte, F. Loeser: Non-archimedean Yomdin-Gromov parametrizations and points of bounded height, Forum of Mathematics, Pi,
doi:10.1017/fmp.2015.4, Vol. 3, e5, 60 pages (2015).
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, Journal of Fourier Analysis and Applications, DOI 10.1007/s00041-015-9421-2 (2015).
R. Cluckers, F. Loeser: Motivic integration in all residue field characteristics for Henselian
discretely valued fields of characteristic zero, J. für die reine und
angewandte Mathematik, DOI 10.1515/ crelle-2013-0025, Vol. 701, 1--31 (2015).
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, Inventiones Mathematicae, DOI 10.1007/s00222-015-0583-y (2015).
R. Cluckers, J. Gordon, I. Halupczok: Motivic functions, integrability, and applications to harmonic analysis on p-adic groups., Electronic Research Announcements in Math. (ERA), Vol. 21, 137--152 (2014).
R. Cluckers, J. Gordon, I. Halupczok: Integrability of
oscillatory functions on local fields: transfer principles,
Duke Math. J., Vol. 163, No. 8, 1549--1600 (2014).
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, 1163--1195 (2014).
R. Cluckers, F. Loeser, J. Nicaise: Chai's Conjecture and Fubini properties of dimensional motivic integration, Algebra and Number Theory, Vol. 7, No. 4, 893--915 (2013).
R. Cluckers, J. Derakhshan, E. Leenknegt, A. Macintyre: Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields, Annals of Pure and Applied Logic, Vol. 164,
No. 12, 1236--1246 (2013).
R. Cluckers, D. J. Miller: Lebesgue classes and preparation of real constructible functions, Journal of Functional Analysis (JFA), Vol. 264, No. 7, 1599--1642 (2013).
R. Cluckers, I. Halupczok: Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry, Selecta Mathematica, doi: 10.1007/s00029-012-0088-0 (2012).
R. Cluckers, G. Comte, F. Loeser Local metric properties and regular stratifications of p-adic definable sets Comment. Math. Helv., Vol. 87, No. 4, 963--1009 (2012).
R. Cluckers, E. Leenknegt A version of p-adic minimality, J. Symbolic Logic, Vol. 77, No. 2, 621--630 (2012).
R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, Confluentes Mathematici,
Vol. 3, No 4, 587--615 (2011), doi: 10.1142/S1793744211000473.
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
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
R. Cluckers, J. Nicaise and J. Sebag (Editors): Motivic integration and its interactions
with model theory and non-archimedean geometry Volume 2, Cambridge University
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, C. Cunningham, J. Gordon, L. Spice: On the computability of some positive-depth characters near the identity, Representation Theory,
Vol. 15, 531--567 (2011).
R. Cluckers: Analytic van der Corput Lemma for p-adic and F_q((t)) oscillatory integrals, singular Fourier transforms,
and restriction theorems, Expositiones Mathematicae, Vol. 29, No. 4, 371--386 (2011),
R. Cluckers, D. J. Miller: Loci of integrability, zero loci,
and stability under integration for constructible functions on Euclidean space with Lebesgue measure,
Int. Math. Res. Not. (IMRN), doi: 10.1093/imrn/rnr133 (2011).
R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur.
Math. Soc. (JEMS), Vol. 13, No. 4, 1147--1223 (2011) arXiv:0908.2376.
R. Cluckers, D. J. Miller: Stability under integration of sums of products of real globally subanalytic functions and their
logarithms, Duke Math. J., Vol. 156, No. 2, 311--348 (2011).
R. Cluckers, G. Comte, F. Loeser: Lipschitz continuity properties for p-adic semi-algebraic and subanalytic functions, GAFA (Geometric and Functional Analysis),
Vol. 20, No 1, 68--87 (2010).
R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle,
Annals of Mathematics,
Vol. 171, No. 2, 1011-–1065
R. Cluckers: Exponential sums: questions by Denef, Sperber, and
Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 3745--3756 (2010).
Cluckers, F. Loeser: Constructible motivic functions and motivic
integration, Inventiones Mathematicae, Vol. 173, No. 1, 23--121 (2008).
R. Cluckers, L. Lipshitz, Z. Robinson: Real closed fields with nonstandard and standard analytic structure, Journal of the London Mathematical
Society, Vol. 78, No. 1,
R. Cluckers, E. Leenknegt: Rectilinearization of semi-algebraic p-adic sets and Denef's rationality of Poincaré series,
Journal of Number Theory, Vol. 128, No. 7, 2185--2197 (2008).
R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of
Mathematics of Jussieu, Vol. 7, No. 2, 269--289 (2008).
R. Cluckers: An introduction to b-minimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 .
Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 84--92, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL
R. Cluckers: Igusa and Denef-Sperber
conjectures on nondegenerate p-adic exponential sums, Duke Math. J., Vol. 141, No. 1, 205-216 (2008).
R. Cluckers: The modulo p and p˛ cases of the Igusa
Conjecture on exponential sums and the motivic oscillation index, Int. Math. Res. Not. (IMRN), (2008) Vol. 2008, article ID rnm118, 20 pages,
R. Cluckers, F. Loeser: b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195 - 227 (2007).
Cluckers, A. Herremans: Computation of character sums and applications to prehomogeneous vector spaces.
With an appendix "L-functions of prehomogeneous vector spaces" by Fumihiro Sato, Bull. Soc. Math. France, Vol. 135, No. 4, 475-494 (2007).
R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and
J. Pure Appl. Algebra, 208, no. 2, 691 - 698 (2007).
Cluckers, L. Lipshitz, Z. Robinson: Analytic cell decomposition and analytic motivic integration,
Ann. Sci. École Norm. Sup., 39, no. 4, 535 - 568 (2006).
R. Cluckers, F. Loeser: Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de
transfert, Comptes rendus de l'Académie des Sciences, 341, 741 - 746 (2005).
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,
Cluckers: Multivariate Igusa theory: Decay rates of exponential sums, Int. Math. Res. Not. (IMRN), 76 (2004) 4093 - 4108.
- R. Cluckers, F. Loeser: Fonctions
constructible et intégration motivique II, Comptes rendus de l'Académie des Sciences, 339, 487 - 492 (2004).
- R. Cluckers, F. Loeser: Fonctions
constructible et intégration motivique I, Comptes rendus de l'Académie des Sciences, 339,
411 - 416 (2004).
Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, 272, 692
- 700 (2004).
Cluckers: Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc.,
356, no. 4, 1489 - 1499 (2004).
Cluckers: Presburger sets and p-minimal fields, Journal
of Symbolic Logic, 68, no. 1, 153 - 162 (2003).
Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11, 2002 math.LO/0311433.
Cluckers: Cell decomposition and p-adic integration, Thesis
(locally) published in Leuven (2002) math.LO/0301023.
Cluckers: Classification of semi-algebraic p-adic sets up to
semi-algebraic bijection, Journal für die reine und
angewandte Mathematik, 540, 105 -
Cluckers, D. Haskell: Grothendieck rings of Z -valued
fields, Bulletin of Symbolic Logic, 7, no. 2, 262 - 269 (2001).
R. Cluckers, J. Pila, A. Wilkie: Uniform parameterization of subanalytic sets and diophantine applications, submitted, arXiv:1605.05916.
R. Cluckers, G. Comte, D. J. Miller, J.-P. Rolin, T. Servi: Integration of
oscillatory and subanalytic functions, submitted, arxiv:1601.01850.
R. Cluckers, I. Halupczok: Integration, uniform in all fields of p-adic numbers, submitted,
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.
Here are some background notes and some slides on motivic integration and transfer principles, from the ETH Nachdiplom lectures I gave in the spring of 2014.
Abstracts and slides of some of my lectures.
Coming up soon:
R. Cluckers, J. Gordon, I. Halupczok: Bounds and limits for motivic exponential functions and orbital integrals.
Model theory and applications
Mons (Belgium), 16 - 19 January 2017, Scientific Committee.
From 2016 on, Z. Chatzidakis and I organize the monthly seminar day GTM 'Geometry and model theory' at the ENS in Paris.
On the 10th October 2016, a Special day on Motivic integration and non-archimedean geometry is held at the University of Lille, organized with
with Pablo Cubides and Kien Nguyen.
Together with David Bourqui, Johannes Nicaise and Julien Sebag, we organize a conference
Schéma des arcs et singularités in Rennes, France, 21 - 25 November 2016.
With E Baro and F. Point we organize the special session Model Theory and Applications of the Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logrońo, La Rioja, Spain, June 6 - 8 (2016).
The workshop Model Theory in Geometry
and Arithmetic, 12 - 16 May (2014), co-organized with J. Pila and T. Scanlon, and concluding the MSRI Spring 2014 semester program Model
Theory, Arithmetic Geometry and Number Theory.
Oberwolfach Seminar: Motivic Integration, Germany, 13 - 19 October 2013, co-organized with A. Chambert-Loir, F. Loeser, J. Nicaise.
Number Theory, Algebraic Geometry and Model Theory, in honor of Jan Denef,
at the CIRM in Luminy, France, September 12 - 16 (2011), co-organized with J. Nicaise and W. Veys.
Motivic Integration and its Interactions with Model
Theory and Non-Archimedean Geometry
May 12 - May 17, 2008,
ICMS, Edinburgh (UK), co-organized with A. Macintyre, J. Nicaise, and J. Sebag
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.
download my curriculum
vitae and publication list. (Last update: January 2017)
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
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.
Look at my favorite pianist Andrew Hill's website.
Other pianists I admire are
Abdullah Ibrahim, the young Vijay Iyer, and
for example the classical pianist
Sviatoslav Richter (see All Music Guide ).
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.