Raf Cluckers
Directeur de Recherche du CNRS, University of Lille, France.
Associate professor (part time, 20%) at KU Leuven, Belgium.
ERC Consolidator Grant nr. 615722, MOTMELSUM, March 2014  February 2019.
Address:
University of Lille
Laboratoire Painlevé, CNRS  UMR 8524
Cité Scientifique
59655 Villeneuve d'Ascq Cedex (France)
Bureau: 314, building: M2
Email: Raf.Cluckers"at"univlille.fr
URL: http://rcluckers.perso.math.cnrs.fr/
TEL: +33 320434193 and +32 16327025
Secondary address:
KU Leuven,
Departement Wiskunde,
Section of Algebra
Celestijnenlaan 200B
3001 Leuven (Belgium)
Current and former PhD students and Postdocs:
Current PhD students: Siegfried Van Hille (Van Hille is cosupervised by Wim Veys).
Former PhD students: Saskia Chambille, Tristan Kuijpers, Eva Leenknegt, Alexander Lemmens, Kien Huu Nguyen (Chambille was cosupervised by Wim Veys, Lemmens was cosupervised by Wouter Castryck).
Current postdocs: Eva Leenknegt, Kien Huu Nguyen, Philip Dittmann.
Former postdocs: Jorge Cely, Pablo Cubides, Arne Smeets, Dmitry Sustretov, and Wouter Castryck.
Published* papers and books:

R. Cluckers, J. Gordon, I. Halupczok: Uniform analysis on local fields and applications to orbital integrals, Trans. Amer. Math. Soc. Ser. B, Vol. 5, 125166 doi.org/10.1090/btran/25 (2018).

E. Hrushovski, B. Martin, S. Rideau: Definable equivalence relations and zeta functions of groups
(with an appendix by Raf Cluckers), J. Eur. Math. Soc. (JEMS), Vol. 20, No. 10, 24672537 DOI: 10.4171/JEMS/817 (2018).

R. Cluckers, I. Halupczok, F. Loeser, M. Raibaut, Distributions and wave front sets in the uniform nonarchimedean setting, Trans. London Math. Soc., DOI:10.1112/tlm3.12013 (2018).

R. Cluckers, G. Comte, D. J. Miller, J.P. Rolin, T. Servi: Integration of
oscillatory and subanalytic functions, Duke Math. Journal, Vol. 167, no. 7, 12391309 doi:10.1215/0012709420170056 (2018).

R. Cluckers, I. Halupczok: Integration of functions of motivic exponential class, uniform in all nonarchimedean local fields of characteristic zero, J. Éc. polytech. Math. (JEP), Vol. 5, 4578 doi: 10.5802/jep.63 (2018).

R. Cluckers, F. Martin: A definable, padic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps, J. Inst. Math. Jussieu, Vol. 17, no. 1, 3957,
doi:10.1017/S1474748015000390, 119 (2018), © Cambridge University Press.

R. Cluckers, I. Halupczok: Definable sets up to definable bijections in Presburger groups, Trans. London Math. Soc., Vol. 5, no. 1, 4770 doi: 10.1112/tlm3.12011 (2018).

R. Cluckers, L. Lipshitz: Strictly Convergent Analytic Structures, J. Eur.
Math. Soc. (JEMS), Vol. 19, no. 1, 107149 (2017).

R. Cluckers, W. Veys: Bounds for
padic exponential sums and logcanonical thresholds, Amer. J. Math., Vol. 138, No. 1, 6180 (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
23659564, Springer (2016).

S.W. Shin, N. Templier: SatoTate theorem for families and lowlying zeros of automorphic Lfunctions, with appendix A by R. Kottwitz and Appendix B by R. Cluckers, J. Gordon and I. Halupczok, Inventiones Mathematicae, Vol. 203, no. 1, 1177, DOI 10.1007/s002220150583y (2016).

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, Vol. 22, No. 1, 215236, DOI 10.1007/s0004101594212 (2016).

R. Cluckers, G. Comte, F. Loeser: Nonarchimedean YomdinGromov parametrizations and points of bounded height, Forum of Mathematics, Pi,
Vol. 3, e5, 60 pages, doi:10.1017/fmp.2015.4 (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/ crelle20130025, Vol. 701, 131 (2015).

R. Cluckers, J. Gordon, I. Halupczok: Motivic functions, integrability, and applications to harmonic analysis on padic groups., Electronic Research Announcements in Math. (ERA), Vol. 21, 137152 (2014).

R. Cluckers, J. Gordon, I. Halupczok: Integrability of
oscillatory functions on local fields: transfer principles,
Duke Math. J., Vol. 163, No. 8, 15491600 (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, 11631195 (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, 893915 (2013).

R. Cluckers, J. Derakhshan, E. Leenknegt, A. Macintyre: Uniformly defining valuation rings in Henselian valued fields with finite or pseudofinite residue fields, Annals of Pure and Applied Logic, Vol. 164,
No. 12, 12361246 (2013).

R. Cluckers, D. J. Miller: Lebesgue classes and preparation of real constructible functions, Journal of Functional Analysis (JFA), Vol. 264, No. 7, 15991642 (2013).

R. Cluckers, I. Halupczok: Approximations and Lipschitz continuity in padic semialgebraic and subanalytic geometry, Selecta Mathematica, Vol. 18, No. 4, 825837, doi: 10.1007/s0002901200880 (2012).

R. Cluckers, G. Comte, F. Loeser Local metric properties and regular stratifications of padic definable sets Comment. Math. Helv., Vol. 87, No. 4, 9631009 (2012).

R. Cluckers, E. Leenknegt A version of padic minimality, J. Symbolic Logic, Vol. 77, No. 2, 621630 (2012).

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), No. 14, 31823191, doi: 10.1093/imrn/rnr133 (2012).

R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, Confluentes Mathematici,
Vol. 3, No 4, 587615, doi: 10.1142/S1793744211000473 (2011).

R. Cluckers, Y. de Cornulier, N. Louvet, R. Tessera, A. Valette: The HoweMoore property for real and padic groups, Math. Scand., Vol. 109, No. 2, 201224
(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 nonarchimedean 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 nonarchimedean geometry, Volume 1, Cambridge University
Press (2011).

R. Cluckers, J. Nicaise and J. Sebag (Editors): Motivic integration and its interactions
with model theory and nonarchimedean 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: 9781571462275, (2011).

R. Cluckers, C. Cunningham, J. Gordon, L. Spice: On the computability of some positivedepth characters near the identity, Representation Theory,
Vol. 15, 531567 (2011).

R. Cluckers: Analytic van der Corput Lemma for padic and F_q((t)) oscillatory integrals, singular Fourier transforms,
and restriction theorems, Expositiones Mathematicae, Vol. 29, No. 4, 371386 (2011),
doi:10.1016/j.exmath.2011.06.004 (2011).

R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur.
Math. Soc. (JEMS), Vol. 13, No. 4, 11471223 (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, 311348 (2011).

R. Cluckers, G. Comte, F. Loeser: Lipschitz continuity properties for padic semialgebraic and subanalytic functions, GAFA (Geometric and Functional Analysis),
Vol. 20, No 1, 6887 (2010).

R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle,
Annals of Mathematics,
Vol. 171, No. 2, 1011–1065
(2010).

R. Cluckers: Exponential sums: questions by Denef, Sperber, and
Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 37453756 (2010).
 R.
Cluckers, F. Loeser: Constructible motivic functions and motivic
integration, Inventiones Mathematicae, Vol. 173, No. 1, 23121 (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,
198–212 (2008).

R. Cluckers, E. Leenknegt: Rectilinearization of semialgebraic padic sets and Denef's rationality of Poincaré series,
Journal of Number Theory, Vol. 128, No. 7, 21852197 (2008).

R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of
Mathematics of Jussieu, Vol. 7, No. 2, 269289 (2008).

R. Cluckers: An introduction to bminimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 .
 R.
Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 8492, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL
(2008).

R. Cluckers: Igusa and DenefSperber
conjectures on nondegenerate padic exponential sums, Duke Math. J., Vol. 141, No. 1, 205216 (2008).

R. Cluckers: The modulo p and p² cases of the Igusa
Conjecture on exponential sums and the motivic oscillation index, Int. Math. Res. Not. (IMRN), Vol. 2008, article ID rnm118, 20 pages,
doi:10.1093/imrn/rnm118 (2008).

R. Cluckers, F. Loeser: bminimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195  227 (2007).
 R.
Cluckers, A. Herremans: Computation of character sums and applications to prehomogeneous vector spaces.
With an appendix "Lfunctions of prehomogeneous vector spaces" by Fumihiro Sato, Bull. Soc. Math. France, Vol. 135, No. 4, 475494 (2007).

R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and
dimension,
J. Pure Appl. Algebra, 208, no. 2, 691  698 (2007).
 R.
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).
 R.
Cluckers, F. Loeser: AxKochenErsov Theorems for padic 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: 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).
 R.
Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, 272, 692
 700 (2004).
 R.
Cluckers: Analytic padic cell decomposition and integrals, Trans. Amer. Math. Soc.,
356, no. 4, 1489  1499 (2004).
 R.
Cluckers: Presburger sets and pminimal fields, Journal
of Symbolic Logic, 68, no. 1, 153  162 (2003).
 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 padic integration, Thesis
(locally) published in Leuven (2002) math.LO/0301023.
 R.
Cluckers: Classification of semialgebraic padic sets up to
semialgebraic bijection, Journal für die reine und
angewandte Mathematik, 540, 105 
114 (2001).
 R.
Cluckers, D. Haskell: Grothendieck rings of Z valued
fields, Bulletin of Symbolic Logic, 7, no. 2, 262  269 (2001).
Preprints:

R. Cluckers, M. Mustata: An invariant detecting rational singularities via the log canonical threshold, arXiv:1901.08111.

R. Cluckers, M. Mustata, K. H. Nguyen: Igusa's conjecture for exponential sums: optimal estimates for nonrational singularities, arXiv:1810.11340.

R. Cluckers, J. Pila, A. Wilkie: Uniform parameterization of subanalytic sets and diophantine applications, to appear in Ann. Sci. Ecole Norm. Sup. arXiv:1605.05916.
Coming up soon:

R. Cluckers, I. Halupczok, S. Rideau: Hensel minimality.

A. Aizenbud, R. Cluckers: WFholonomicity of distributions of Cexp class.

G. Binyamini, R. Cluckers, D. Novikov: Finiteness of the number of complex polynomials of bounded degree on the transcendental part of nonarchimedean subanalytic sets.

W. Castryck, R. Cluckers, Ph. Dittmann, K. H. Nguyen, A. Smeets: title coming soon.

R. Cluckers, A. Forey, F. Loeser: Lipschitz continuity, YomdinGromov parametrizations and point counting in valued fields.

R. Cluckers, O. Friedland, Y. Yomdin: title coming soon.

R. Cluckers, I. Halupczok: Evaluation and specialization of motivic functions and nonnullity.

R. Cluckers, I. Halupczok: KontsevichZagier questions for padic integrals.

R. Cluckers, F. Loeser: Motivic Mellin transformation.
Organized Conferences and seminars, and editorial work:

Since 2018, I'm an editor of JEP, Journal de l'École polytechnique Mathématiques.

From 2017 on, C. Michaux, F. Point, I.Halupczok, K. Tent, M. Hils and I organize the biannual seminar days RDMTA, 'Regional Days on Model Theory and Applications'.

From 2016 on, Z. Chatzidakis and I organize the monthly seminar day GTM, 'Geometry and Model Theory', at the ENS in Paris.

Model theory and applications
Mons (Belgium), 16  19 January 2017, Scientific Committee.

Special day on Motivic integration and nonarchimedean geometry, University of Lille, October 10 (2016), Scientific Committee.

Together with David Bourqui, Johannes Nicaise and Julien Sebag, we organized the conference
Schéma des arcs et singularités in Rennes, France, November 21  25 (2016).

With E Baro and F. Point we organized the special session Model Theory and Applications of the Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño, La Rioja, Spain, June 6  8 (2016).

The workshop Model Theory in Geometry
and Arithmetic, 12  16 May (2014), coorganized 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, coorganized with A. ChambertLoir, F. Loeser, J. Nicaise.

The conference
Number Theory, Algebraic Geometry and Model Theory, in honor of Jan Denef,
at the CIRM in Luminy, France, September 12  16 (2011), coorganized with J. Nicaise and W. Veys.

The Workshop
Motivic Integration and its Interactions with Model
Theory and NonArchimedean Geometry
May 12  May 17, 2008,
ICMS, Edinburgh (UK), coorganized with A. Macintyre, J. Nicaise, and J. Sebag
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.
Curriculum Vitae:
download my curriculum
vitae and publication list. (Last update: February 2019)
Current projects:
One of my most ambitious projects was to solve
Igusa's 1974 conjecture on exponential sums. This is now achieved to a large extent in my recent work with Mustata and Nguyen ! The conjecture describes uniform upper bounds for exponential sums with summation set running over integers modulo any power of any prime 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, and, the recent book by ChambertLoir, Nicaise and Sebag.
Visits and honors:
During the spring term of 2014, I gave the NachdiplomLectures 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 nonarchimedean 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.
Personal items:
Look at my favorite pianist Andrew Hill's website.
Other pianists I admire are, among others,
Joep Beving,
Abdullah Ibrahim, Vijay Iyer, and
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 have been guests in the studios of the national Belgian Radio 1, and,
a warming up program for Arno, but mostly we performed in bars, at parties, and in small concert avenues.
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