Raf Cluckers

ERC Consolidator Grant nr. 615722, MOTMELSUM, 2014 - 2019.

Université Lille 1 Sciences et Technologies
Laboratoire Painlevé, CNRS - UMR 8524
Cité Scientifique
59655 Villeneuve d'Ascq Cedex (France)
Bureau: 314, building: M2
Secondary address:
Algebraic Geometry and Number Theory
Departement Wiskunde
Universiteit Leuven
Celestijnenlaan 200B
3001 Leuven (Belgium)
Bureau: 01.27
E-mail: Raf.Cluckers"at"math.univ-lille1.fr and Raf.Cluckers"at"wis.kuleuven.be
URL: http://math.univ-lille1.fr/~cluckers
TEL: +33 320434193 and +32 16327025

Published papers and books:

  1. R. Cluckers, J. Gordon, I. Halupczok: Motivic functions, integrability, and uniform in p bounds for orbital integrals, Electronic Research Announcements in Math. (ERA), Vol. 21, 137--152 (2014).
  2. 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).
  3. 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).
  4. 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).
  5. 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).
  6. 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).
  7. 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).
  8. 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).
  9. R. Cluckers, E. Leenknegt A version of p-adic minimality, J. Symbolic Logic, Vol. 77, No. 2, 621--630 (2012).
  10. R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, Confluentes Mathematici, Vol. 3, No 4, 587--615 (2011), doi: 10.1142/S1793744211000473.
  11. 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.
  12. 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.
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. 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), doi:10.1016/j.exmath.2011.06.004 (2011).
  18. 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).
  19. R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur. Math. Soc. (JEMS), Vol. 13, No. 4, 1147--1223 (2011) arXiv:0908.2376.
  20. 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).
  21. 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).
  22. R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle, Annals of Mathematics, Vol. 171, No. 2, 1011-–1065 (2010).
  23. R. Cluckers: Exponential sums: questions by Denef, Sperber, and Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 3745--3756 (2010).
  24. R. Cluckers, F. Loeser: Constructible motivic functions and motivic integration, Inventiones Mathematicae, Vol. 173, No. 1, 23--121 (2008).
  25. 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).
  26. 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).
  27. R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of Mathematics of Jussieu, Vol. 7, No. 2, 269--289 (2008).
  28. R. Cluckers: An introduction to b-minimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 .
  29. R. Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 84--92, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL (2008).
  30. R. Cluckers: Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums, Duke Math. J., Vol. 141, No. 1, 205-216 (2008).
  31. 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), (2008) Vol. 2008, article ID rnm118, 20 pages, doi:10.1093/imrn/rnm118.
  32. R. Cluckers, F. Loeser: b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195 - 227 (2007).
  33. R. 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).
  34. R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and dimension, J. Pure Appl. Algebra, 208, no. 2, 691 - 698 (2007).
  35. R. Cluckers, L. Lipshitz, Z. Robinson: Analytic cell decomposition and analytic motivic integration, Ann. Sci. École Norm. Sup., 39, no. 4, 535 - 568 (2006).
  36. 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).
  37. 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.
  38. R. Cluckers: Multivariate Igusa theory: Decay rates of exponential sums, Int. Math. Res. Not. (IMRN), 76 (2004) 4093 - 4108.
  39. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique II, Comptes rendus de l'Académie des Sciences, 339, 487 - 492 (2004).
  40. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique I, Comptes rendus de l'Académie des Sciences, 339, 411 - 416 (2004).
  41. R. Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, 272, 692 - 700 (2004).
  42. R. Cluckers: Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc., 356, no. 4, 1489 - 1499 (2004).
  43. R. Cluckers: Presburger sets and p-minimal fields, Journal of Symbolic Logic, 68, no. 1, 153 - 162 (2003).
  44. R. Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11, 2002 math.LO/0311433.
  45. R. Cluckers: Cell decomposition and p-adic integration, Thesis (locally) published in Leuven (2002) math.LO/0301023.
  46. 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.
  47. R. Cluckers, D. Haskell: Grothendieck rings of Z -valued fields, Bulletin of Symbolic Logic, 7, no. 2, 262 - 269 (2001).
Preprints and notes:
  1. R. Cluckers, F. Martin: A definable, p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps, submitted, arXiv:1502.03036.
  2. R. Cluckers, J. Gordon, I. Halupczok: Transfer principles for Bounds of motivic exponential functions, submitted, arXiv:1412.4573.
  3. R. Cluckers, G. Comte, F. Loeser: Non-archimedean Yomdin-Gromov parametrizations and points of bounded height, submitted, arXiv:1404.1952.
  4. R. Cluckers, L. Lipshitz: Strictly Convergent Analytic Structures, to appear in J. Eur. Math. Soc. (JEMS), arXiv:1312.5932.
  5. R. Cluckers, growing notes on Motivic integration and transfer principles, ETH Nachdiplom lectures spring 2014.
  6. R. Cluckers, W. Veys: Bounds for p-adic exponential sums and log-canonical thresholds, to appear in Amer. J. Math., arXiv:1406.0646.
  7. R. Cluckers, F. Loeser: Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero, to appear in J. für die reine und angewandte Mathematik, arXiv:1102.3832.
  8. 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.
  9. 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.
  10. 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.
  11. Abstracts and slides of some of my lectures.

Coming up soon:

  1. R. Cluckers, G. Comte, D. J. Miller, J.-P. Rolin, T. Servi: Lebesgue integration of the oscillating exponential and subanalytic functions.
Organized Conferences:
  1. 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.
  2. Oberwolfach Seminar: Motivic Integration, Germany, 13 - 19 October 2013, co-organized with A. Chambert-Loir, F. Loeser, J. Nicaise.
  3. The conference 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.
  4. The Workshop 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.

Curriculum Vitae: download my curriculum vitae and publication list. (Last update: February 2015)

Current Postdocs and PhD students:

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.

Personal items:

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.