Raf Cluckers

ERC Consolidator Grant 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, Raf.Cluckers"at"wis.kuleuven.be
URL: http://math.univ-lille1.fr/~cluckers
TEL: 0032 16327025

Published papers and books:

  1. 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).
  2. 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).
  3. 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).
  4. 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).
  5. 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).
  6. R. Cluckers, E. Leenknegt A version of p-adic minimality, J. Symbolic Logic, Vol. 77, No. 2, 621--630 (2012).
  7. R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, Confluentes Mathematici, Vol. 3, No 4, 587--615 (2011), doi: 10.1142/S1793744211000473.
  8. 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.
  9. 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.
  10. 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).
  11. 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).
  12. 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).
  13. 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).
  14. 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).
  15. 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).
  16. R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur. Math. Soc. (JEMS), Vol. 13, No. 4, 1147--1223 (2011) arXiv:0908.2376.
  17. 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).
  18. 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).
  19. R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle, Annals of Mathematics, Vol. 171, No. 2, 1011-–1065 (2010).
  20. R. Cluckers: Exponential sums: questions by Denef, Sperber, and Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 3745--3756 (2010).
  21. R. Cluckers, F. Loeser: Constructible motivic functions and motivic integration, Inventiones Mathematicae, Vol. 173, No. 1, 23--121 (2008).
  22. 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).
  23. 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).
  24. R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of Mathematics of Jussieu, Vol. 7, No. 2, 269--289 (2008).
  25. R. Cluckers: An introduction to b-minimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 .
  26. R. Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 84--92, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL (2008).
  27. R. Cluckers: Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums, Duke Math. J., Vol. 141, No. 1, 205-216 (2008).
  28. 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.
  29. R. Cluckers, F. Loeser: b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195 - 227 (2007).
  30. 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).
  31. R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and dimension, J. Pure Appl. Algebra, 208, no. 2, 691 - 698 (2007).
  32. R. Cluckers, L. Lipshitz, Z. Robinson: Analytic cell decomposition and analytic motivic integration, Ann. Sci. École Norm. Sup., 39, no. 4, 535 - 568 (2006).
  33. 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).
  34. 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.
  35. R. Cluckers: Multivariate Igusa theory: Decay rates of exponential sums, Int. Math. Res. Not. (IMRN), 76 (2004) 4093 - 4108.
  36. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique II, Comptes rendus de l'Académie des Sciences, 339, 487 - 492 (2004).
  37. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique I, Comptes rendus de l'Académie des Sciences, 339, 411 - 416 (2004).
  38. R. Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, 272, 692 - 700 (2004).
  39. R. Cluckers: Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc., 356, no. 4, 1489 - 1499 (2004).
  40. R. Cluckers: Presburger sets and p-minimal fields, Journal of Symbolic Logic, 68, no. 1, 153 - 162 (2003).
  41. R. Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11, 2002 math.LO/0311433.
  42. R. Cluckers: Cell decomposition and p-adic integration, Thesis (locally) published in Leuven (2002) math.LO/0301023.
  43. 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.
  44. 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, G. Comte, F. Loeser: Non-archimedean Yomdin-Gromov parametrizations and points of bounded height, arXiv:1404.1952.
  2. R. Cluckers, L. Lipshitz: Strictly Convergent Analytic Structures, submitted, arXiv:1312.5932.
  3. R. Cluckers, growing notes on Motivic integration and transfer principles, ETH Nachdiplom lectures spring 2014.
  4. 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.
  5. R. Cluckers, J. Gordon, I. Halupczok: Integrability of oscillatory functions on local fields: transfer principles, to appear in Duke Math. J., arXiv:1111.4405.
  6. R. Cluckers, J. Gordon, I. Halupczok: Local integrability results in harmonic analysis on reductive groups in large positive characteristic, to appear in Ann. Sci. Ecole Norm. Sup., arXiv:1111.7057.
  7. R. Cluckers, J. Gordon, I. Halupczok: Motivic functions, integrability, and uniform in p bounds for orbital integrals, to appear in Electronic Research Announcements in Math. (ERA), arXiv:1309.0594.
  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, submitted, 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. Abstracts and slides of some of my lectures.

Coming up soon:

  1. R. Cluckers, W. Veys: Uniform bounds for p-adic exponential sums.
  2. E. Hrushovski, B. Martin, S. Rideau: Zeta Functions from Definable Equivalence Relations. With an appendix "Rationality results for p-adic subanalytic equivalence relations" by R. Cluckers.
Organized Conferences:
  1. With J. Pila and T. Scanlon we organize the workshop Model Theory in Geometry and Arithmetic which will conclude the MSRI Spring 2014 semester program Model Theory, Arithmetic Geometry and Number Theory.
  2. Together with A. Chambert-Loir, F. Loeser, J. Nicaise we organize a course on motivic integration in Oberwolfach to be held in 2013.
  3. Together with J. Nicaise and W. Veys we organized the conference Number Theory, Algebraic Geometry and Model Theory, in honor of Jan Denef, at the CIRM in Luminy, France, September 12 - 16 (2011).
  4. Together with A. Macintyre, J. Nicaise, and J. Sebag we organized the Workshop on Motivic Integration: Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry May 12 - May 17, 2008, ICMS, 14, India Street, Edinburgh.

I started my Ph.D. studies in 1999 in Leuven under supervision of Prof. Dr. J. Denef, finishing in 2002. Since all chapters of the thesis are published in journals by now I recommend authors to refer to the published papers.

Curriculum Vitae: download my curriculum vitae and publication list as a pdf-file. (Last update: September 2013)

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 semester of 2014, I will give the Nachdiplom-Lectures at the ETH Zürich. I will be a MSRI Research Member in May 2014, Berkeley. I obtained an ERC Consolidator Grant with title "Motivic Mellin transforms and exponential sums through non-archimedean geometry" 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.