Raf Cluckers

Published papers and books:

1. 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.
2. 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.
3. 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).
4. 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).
5. 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).
6. 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).
7. 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) arXiv:1001.2013.
8. 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).
9. R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur. Math. Soc. (JEMS), Vol. 13, No. 4, 1147--1223 (2011) arXiv:0908.2376.
10. 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) arXiv:0911.4373.
11. 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) arXiv:0904.3853.
12. R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle, Annals of Mathematics, Vol. 171, No. 2, 1011-–1065 (2010) math.AG/0512022.
13. R. Cluckers: Exponential sums: questions by Denef, Sperber, and Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 3745--3756 (2010) arXiv:0711.3365.
14. R. Cluckers, F. Loeser: Constructible motivic functions and motivic integration, Inventiones Mathematicae, Vol. 173, No. 1, 23--121 (2008) math.AG/0410203.
15. 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) math.LO/0610666.
16. 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).
17. R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of Mathematics of Jussieu, Vol. 7, No. 2, 269--289 (2008) math.AG/0703704.
18. R. Cluckers: An introduction to b-minimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 .
19. R. Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 84--92, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL (2008).
20. R. Cluckers: Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums, Duke Math. J., Vol. 141, No. 1, 205-216 (2008) math.NT/0606269.
21. 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 math.NT/0602438.
22. R. Cluckers, F. Loeser: b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195 - 227 (2007) math.LO/0610183.
23. 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) math.NT/0408139.
24. R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and dimension, J. Pure Appl. Algebra, 208, no. 2, 691 - 698 (2007) math.LO/0607165.
25. R. Cluckers, L. Lipshitz, Z. Robinson: Analytic cell decomposition and analytic motivic integration, Ann. Sci. École Norm. Sup., 39, no. 4, 535 - 568 (2006) math.AG/0503722.
26. 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), math.NT/0509723.
27. 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.
28. R. Cluckers: Multivariate Igusa theory: Decay rates of exponential sums, Int. Math. Res. Not. (IMRN), 76 (2004) 4093 - 4108 math.NT/0306351.
29. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique II, Comptes rendus de l'Académie des Sciences, 339, 487 - 492 (2004), math.AG/0403350.
30. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique I, Comptes rendus de l'Académie des Sciences, 339, 411 - 416 (2004), math.AG/0403349.
31. R. Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, 272, 692 - 700 (2004), math.LO/0210350.
32. R. Cluckers: Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc., 356, no. 4, 1489 - 1499 (2004), math.NT/0206161.
33. R. Cluckers: Presburger sets and p-minimal fields, Journal of Symbolic Logic, 68, no. 1, 153 - 162 (2003) math.LO/0206197.
34. R. Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11, 2002 math.LO/0311433.
35. R. Cluckers: Cell decomposition and p-adic integration, Thesis (locally) published in Leuven (2002) math.LO/0301023.
36. 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.
37. R. Cluckers, D. Haskell: Grothendieck rings of Z -valued fields, Bulletin of Symbolic Logic, 7, no. 2, 262 - 269 (2001), math.LO/0311435.

1. R. Cluckers, J. Gordon, I. Halupczok: Transfer principles for integrability and boundedness conditions for motivic exponential functions, submitted, arXiv:1111.4405.
2. R. Cluckers, J. Gordon, I. Halupczok: Definability results for invariant distributions on a reductive unramified p-adic group, submitted, arXiv:1111.7057.
3. R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, to appear in Confluentes Mathematici, arXiv:1110.3200.
4. R. Cluckers, F. Loeser: Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero, submitted, arXiv:1102.3832.
5. R. Cluckers, F. Loeser, J. Nicaise: Chai's Conjecture and Fubini properties of dimensional motivic integration, submitted, arXiv:1102.5653.
6. R. Cluckers, E. Leenknegt: A version of p-adic minimality, to appear in JSL, Journal of Symbolic Logic.
7. R. Cluckers, I. Halupczok: Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry, to appear in Selecta Mathematica, arXiv:1009.3414.
8. R. Cluckers, G. Comte, F. Loeser: Local metric properties and regular stratifications of p-adic definable sets, to appear in CMH, Commentarii Mathematici Helvetici, arXiv:0910.0799.
9. Abstracts and slides of some of my lectures.

Coming up soon:

1. R. Cluckers, D. J. Miller: Diagrams of Lebesgue classes of real constructible functions.
2. R. Cluckers, D. J. Miller: Bounding decay rates of families of generalized Fourier transforms of constructible functions.

1. Together with J. Nicaise and W. Veys we organized the conference Number Theory, Algebraic Geometry and Model Theory, in honour of Jan Denef, at the CIRM in Luminy, France, September 12 - 16 (2011).
2. 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.

Thesis:
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 as a pdf-file. (Last update: December 2011)

With D. J. Miller we construct algebras of functions over the reals which are closed under integration, similarly as in arXiv:0911.4373 and (motivically) as in math.AG/0410203.

With J. Gordon and I. Halupczok we study transfer principles (that is, results about changing the characteristic of local non-archimedean fields) for integrability conditions.

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.

In 2011, I was awarded with a "prime d'excellence" by the CNRS of France. I was in the final short list for the Sacks Prize 2004 of the Association for Symbolic Logic for the best Ph.D. thesis. I was classified on the third place in the contest Concours Chercheurs CR1 2007 du CNRS in France (chargé de recherche de 1re classe, concours 01/04), and on the first place in 2008. I have been nominated for best teaching assistant for math in Leuven. Further I won the first prize on the Belgian national contest "Axion Classics" for classical piano for young non professionals 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.