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:
CNRS, University of Lille
Laboratoire Painlevé - UMR 8524
Cité Scientifique
59655 Villeneuve d'Ascq Cedex (France)
Bureau: 314, building: M2
E-mail: Raf.Cluckers"at"univ-lille.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)

PhD students and Postdocs:

Current PhD students: Siegfried Van Hille, Floris Vermeulen (Van Hille is co-supervised by Wim Veys).

Former PhD students: Saskia Chambille, Tristan Kuijpers, Eva Leenknegt, Alexander Lemmens, Kien Huu Nguyen (Chambille was co-supervised by Wim Veys, Lemmens was co-supervised by Wouter Castryck).

Current postdocs: Eva Leenknegt, Kien Huu Nguyen, Victoria Cantoral Farfan.

Former postdocs: Wouter Castryck, Jorge Cely, Pablo Cubides, Philip Dittmann, Arne Smeets, Dmitry Sustretov.

Published papers*:

  1. A. Aizenbud, R. Cluckers: Wave front holonomicity of Cexp class distributions on non-archimedean local fields, Forum of Mathematics, Sigma, Vol. 8, e35, doi:org/10.1017/fms.2020.27 (2020).
  2. R. Cluckers, J. Pila, A. Wilkie: Uniform parameterization of subanalytic sets and diophantine applications, Ann. Sci. Ecole Norm. Sup., Vol. 53, No. 1, 1--42 doi.10.24033/asens.2416 (2020).
  3. R. Cluckers, M. Mustata, K. H. Nguyen: Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities, Forum of Mathematics, Pi, Vol. 7, e3, doi:10.1017/fmp.2019.3 (2019).
  4. R. Cluckers, J. Gordon, I. Halupczok: Uniform analysis on local fields and applications to orbital integrals, Trans. Amer. Math. Soc. Ser. B, Vol. 5, 125--166 doi.org/10.1090/btran/25 (2018).
  5. 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, 2467--2537 doi:10.4171/JEMS/817 (2018).
  6. R. Cluckers, I. Halupczok, F. Loeser, M. Raibaut, Distributions and wave front sets in the uniform non-archimedean setting, Trans. London Math. Soc., doi:10.1112/tlm3.12013 (2018).
  7. 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, 1239--1309 doi:10.1215/00127094-2017-0056 (2018).
  8. R. Cluckers, I. Halupczok: Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero, J. Éc. polytech. Math. (JEP), Vol. 5, 45--78 doi: 10.5802/jep.63 (2018).
  9. R. Cluckers, F. Martin: A definable, p-adic analogue of Kirszbraun's Theorem on extensions of Lipschitz maps, J. Inst. Math. Jussieu, Vol. 17, no. 1, 39--57, doi:10.1017/S1474748015000390, 1--19, © Cambridge University Press (2018).
  10. R. Cluckers, I. Halupczok: Definable sets up to definable bijections in Presburger groups, Trans. London Math. Soc., Vol. 5, no. 1, 47--70 doi:10.1112/tlm3.12011 (2018).
  11. R. Cluckers, L. Lipshitz: Strictly Convergent Analytic Structures, J. Eur. Math. Soc. (JEMS), Vol. 19, no. 1, 107--149 doi: 10.4171/JEMS/662 (2017).
  12. R. Cluckers, W. Veys: Bounds for p-adic exponential sums and log-canonical thresholds, Amer. J. Math., Vol. 138, No. 1, 61--80 doi: 10.1353/ajm.2016.0003 (2016).
  13. R. Cluckers, J. Gordon, I. Halupczok: Transfer principles for Bounds of motivic exponential functions, doi: 10.1007/978-3-319-41424-9_3 bookchapter in Families of automorphic forms and the trace formula, Müller, Werner, Shin, Sug Woo, Templier, Nicolas (Eds.) Simons Symp. ISSN 2365-9564, Springer (2016).
  14. 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, Vol. 203, no. 1, 1--177, doi: 10.1007/s00222-015-0583-y (2016).
  15. 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, 215--236, doi: 10.1007/s00041-015-9421-2 (2016).
  16. R. Cluckers, G. Comte, F. Loeser: Non-archimedean Yomdin-Gromov parametrizations and points of bounded height, Forum of Mathematics, Pi, Vol. 3, e5, 60 pages doi:10.1017/fmp.2015.4 (2015).
  17. 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, Vol. 701, 1--31 doi:10.1515/crelle-2013-0025 (2015).
  18. 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 doi:10.3934/era.2014.21.137 (2014).
  19. R. Cluckers, J. Gordon, I. Halupczok: Integrability of oscillatory functions on local fields: transfer principles, Duke Math. J., Vol. 163, No. 8, 1549--1600 doi:10.1215/00127094-2713482 (2014).
  20. 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 doi:10.24033/asens.2236 (2014).
  21. 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 doi:10.2140/ant.2013.7.893 (2013).
  22. 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 doi:10.1016/j.apal.2013.06.010 (2013).
  23. R. Cluckers, D. J. Miller: Lebesgue classes and preparation of real constructible functions, Journal of Functional Analysis (JFA), Vol. 264, No. 7, 1599--1642 doi:10.1016/j.jfa.2013.01.014 (2013).
  24. R. Cluckers, I. Halupczok: Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry, Selecta Mathematica, Vol. 18, No. 4, 825--837 doi: 10.1007/s00029-012-0088-0 (2012).
  25. 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 doi:10.4171/CMH/275 (2012).
  26. R. Cluckers, E. Leenknegt A version of p-adic minimality, J. Symbolic Logic, Vol. 77, No. 2, 621--630 doi:10.2178/jsl/1333566641 (2012).
  27. 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, 3182--3191 doi: 10.1093/imrn/rnr133 (2012).
  28. R. Cluckers, I. Halupczok: Quantifier elimination in ordered abelian groups, Confluentes Mathematici, Vol. 3, No 4, 587--615 doi:10.1142/S1793744211000473 (2011).
  29. 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 doi:10.7146/math.scand.a-15185 (2011).
  30. 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 doi:10.1017/cbo9780511667534.008 pdf here (2011).
  31. 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 doi:10.1017/CBO9780511667534 (2011).
  32. 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 doi:10.1017/CBO9780511984433 (2011).
  33. 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).
  34. 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 doi:10.1090/S1088-4165-2011-00403-9 (2011).
  35. 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 doi:10.1016/j.exmath.2011.06.004 (2011).
  36. R. Cluckers, L. Lipshitz: Fields with analytic structure, J. Eur. Math. Soc. (JEMS), Vol. 13, No. 4, 1147--1223 doi:10.4171/JEMS/278 (2011).
  37. 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 doi:10.1215/00127094-2010-213 (2011).
  38. 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 10.1007/s00039-010-0060-0 (2010).
  39. R. Cluckers, F. Loeser: Constructible exponential functions, motivic Fourier transform and transfer principle, Annals of Mathematics, Vol. 171, No. 2, 1011-–1065 doi:10.4007/annals.2010.171.1011 (2010).
  40. R. Cluckers: Exponential sums: questions by Denef, Sperber, and Igusa, Trans. Amer. Math. Soc., Vol. 362, No. 7, 3745--3756 doi:10.1090/S0002-9947-09-05084-3 (2010).
  41. R. Cluckers: An introduction to b-minimality, Conference Proceedings of LC2006, Nijmegen, math.LO/0610928 doi:10.1017/CBO9780511605321.006 (2009).
  42. R. Cluckers, F. Loeser: Constructible motivic functions and motivic integration, Inventiones Mathematicae, Vol. 173, No. 1, 23--121 doi:10.1007/s00222-008-0114-1 (2008).
  43. 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 doi:10.1112/jlms/jdn024 (2008).
  44. 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 doi:10.1016/j.jnt.2007.10.013 (2008).
  45. R. Cluckers, J. Denef: Orbital integrals for linear groups, Journal of the Institute of Mathematics of Jussieu, Vol. 7, No. 2, 269--289 doi:10.1017/S1474748008000029 (2008).
  46. R. Cluckers: Parameterized local zeta functions, Logic Colloquium 2004, 84--92, Lect. Notes Log., 29, Assoc. Symbol. Logic, Chicago, IL doi:10.1017/CBO9780511721151.006 (2008).
  47. R. Cluckers: Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums, Duke Math. J., Vol. 141, No. 1, 205--216 doi:10.1215/S0012-7094-08-14116-X (2008).
  48. 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).
  49. R. Cluckers, F. Loeser: b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195--227 doi:10.1142/S0219061307000664 (2007).
  50. 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 doi:10.24033/bsmf.2543 (2007).
  51. R. Cluckers, M. Edmundo: Integration of positive constructible functions against Euler characteristic and dimension, J. Pure Appl. Algebra, Vol. 208, no. 2, 691--698 doi:10.1016/j.jpaa.2006.03.005 (2007).
  52. R. Cluckers, L. Lipshitz, Z. Robinson: Analytic cell decomposition and analytic motivic integration, Ann. Sci. École Norm. Sup., Vol. 39, no. 4, 535--568 doi:10.1016/j.ansens.2006.03.001 (2006).
  53. R. Cluckers, F. Loeser: Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert, Comptes rendus de l'Académie des Sciences, Vol. 341, 741--746 doi:10.1016/j.crma.2005.10.008 (2005).
  54. 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.), Proceedings of the Miami Conference 2003, math.AG/0410223 doi:10.1007/0-8176-4417-2_5 (2005).
  55. R. Cluckers: Multivariate Igusa theory: Decay rates of exponential sums, Int. Math. Res. Not. (IMRN), Vol. 76, 4093--4108 doi:10.1155/S1073792804141913 (2004).
  56. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique II, Comptes rendus de l'Académie des Sciences, Vol. 339, 487--492 doi:10.1016/j.crma.2004.06.027 (2004).
  57. R. Cluckers, F. Loeser: Fonctions constructible et intégration motivique I, Comptes rendus de l'Académie des Sciences, Vol. 339, 411 - 416 doi:10.1016/j.crma.2004.06.026 (2004).
  58. R. Cluckers: Grothendieck rings of Laurent series fields, J. Algebra, Vol. 272, 692--700 doi:10.1016/S0021-8693(03)00397-1 (2004).
  59. R. Cluckers: Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc., Vol. 356, no. 4, 1489--1499 doi:10.1090/S0002-9947-03-03458-5 (2004).
  60. R. Cluckers: Presburger sets and p-minimal fields, Journal of Symbolic Logic, Vol. 68, no. 1, 153--162 doi:10.1090/S0002-9947-03-03458-5 (2003).
  61. R. Cluckers: Model theory of valued fields, in Model theory and applications, Quaderni di matematica, Vol. 11 math.LO/0311433 (2002).
  62. R. Cluckers: Cell decomposition and p-adic integration, Thesis (locally) published in Leuven math.LO/0301023 (2002).
  63. R. Cluckers, D. Haskell: Grothendieck rings of Z -valued fields, Bulletin of Symbolic Logic, Vol. 7, no. 2, 262 - 269 (2001).
  64. R. Cluckers: Classification of semi-algebraic p-adic sets up to semi-algebraic bijection, Journal für die reine und angewandte Mathematik, Vol. 540, 105--114 doi:10.1515/crll.2001.081 (2001).
Preprints:
  1. R. Cluckers, K. H. Nguyen: Beyond Igusa's conjectures on exponential sums and monodromy, arXiv:2005.04197.
  2. R. Cluckers, I. Halupczok: Evaluation and specialization of motivic functions and non-nullity, arXiv:2004.09981.
  3. R. Cluckers, I. Halupczok: A p-adic variant of Kontsevich--Zagier integral operation rules and of Hrushovski--Kazhdan style motivic integration, arXiv:2003.01500.
  4. R. Cluckers, I. Halupczok, S. Rideau: Hensel minimality, arXiv:1909.13792.
  5. R. Cluckers, M. Mustata: An invariant detecting rational singularities via the log canonical threshold, arXiv:1901.08111.
  6. W. Castryck, R. Cluckers, Ph. Dittmann, K. H. Nguyen: The dimension growth conjecture, polynomial in the degree and without logarithmic factors, to appear in Algebra and Number Theory arXiv:1904.13109.
  7. R. Cluckers, O. Friedland, Y. Yomdin: Doubling coverings via resolution of singularities and preparation, to appear in Communications in Contemporary Mathematics arXiv:1903.04281 doi.org/10.1142/S0219199720500182.
  8. R. Cluckers, A. Forey, F. Loeser: Lipschitz continuity, Yomdin-Gromov parametrizations and point counting in valued fields, to appear in Algebra and Number Theory arXiv:1902.06589.

Coming up soon:

  1. G. Binyamini, R. Cluckers, D. Novikov: Finiteness of the number of complex polynomials of bounded degree on the transcendental part of non-archimedean subanalytic sets.
  2. R. Cluckers, I. Glazer, Y. Hendel : A number theoretic characterization of the FRS property.
  3. R. Cluckers, F. Loeser: Motivic Mellin transformation.
  4. More on: Holonomicity of distributions of Cexp class, motivic integrals, non-archimedean geometry, Mellin transformation, hensel minimality.
Organized Conferences and seminars, and editorial work:
  1. Since 2018, I'm an editor of JEP, Journal de l'École polytechnique Mathématiques.
  2. 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'.
  3. From 2016 on, Z. Chatzidakis and I organize the monthly seminar day GTM, 'Geometry and Model Theory', at the ENS in Paris.
  4. Model theory and applications Mons (Belgium), 16 - 19 January 2017, Scientific Committee.
  5. Special day on Motivic integration and non-archimedean geometry, University of Lille, October 10 (2016), Scientific Committee.
  6. 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).
  7. 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).
  8. 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.
  9. Oberwolfach Seminar: Motivic Integration, Germany, 13 - 19 October 2013, co-organized with A. Chambert-Loir, F. Loeser, J. Nicaise.
  10. 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.
  11. 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

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: Here is my curriculum vitae and publication list. (Last update: September 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 arXiv:1810.11340 with Mustata and Nguyen, see here for a press announcement (or here for a shorter one). The conjecture describes uniform upper bounds for exponential sums with summation set running over integers modulo any power of any prime p. It is useful for estimating major arcs in the circle method for local global principles for polynomials in many variables compared to their degree.

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 Chambert-Loir, Nicaise and Sebag.

Visits and honors:

My co-author Julia Gordon from UBC has won the 2019 Krieger-Nelson Prize for her joint work with Immanuel Halupczok and myself. 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, 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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