jan homepage

p-adic number theory, Igusa's local zeta function and motivic analogues, motivic and p-adic integration, computational number theory of curves, cohomological study of exponential sums, monodromy, toric geometry, Hilbert's tenth problem, quantifier elimination, subanalytic sets and model theory.

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Contact Information

Address

University of Leuven, Department of Mathematics, Celestijnenlaan 200 B,

B-3001 Leuven (Heverlee), Belgium.

Electronic mail address

jan.denef@wis.kuleuven.ac.be

Web address

http://www.wis.kuleuven.ac.be/wis/algebra/denef.html

Office phone : (+32)16-327010

Office fax : (+32)16-327998

Home phone : (+32)16-228587

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Recent Publications (since 1995)

Jan Denef, Proof of a conjecture of Colliot-Thélène, preprint (version of July 11, 2011).

Jan Denef, Algebraic geometric proof of theorems of Ax-Kochen and Eršov. (This is a beamer presentation, a formal paper about this is in preparation.)

Jan Denef, Monomialization of morphisms and p-adic quantifier elimination, preprint (version of March 21, 2011).

Dan Abramovich, Jan Denef, and Kalle Karu, Weak toroidalization over non-closed fields, preprint (15 pages, October 2010), ArXiv: 1010.6171

Raf Cluckers and Jan Denef, Orbital integrals for linear groups, Journal of the Institute of Mathematics of Jussieu, Vol. 7, No. 2, 269--289 (2008).

W. Castryck, J. Denef, F. Vercauteren, Computing zeta functions of nondegenerate curves, IMRP International Mathematics Research Papers 2006, Article ID 72017 (2006), 1-57.

J. Denef, F. Vercauteren, Computing zeta functions of Cab curves using Monsky-Washnitzer cohomology, Finite Fields and Their Applications 12 (2006), 78-102. (See also the errata.)

J. Denef, J. Nicaise, and P. Sargos, Oscillating integrals and Newton polyhedra, Journal d'Analyse Mathématique 95 (2005), 147-172.

J. Denef and F. Vercauteren, An extension of Kedlaya’s algorithm to hyperelliptic curves in characteristic 2, Journal of Cryptology 19 (2006), 1-25. (See also the errata.)

J. Denef and F. Loeser, On some rational generating series occuring in arithmetic geometry, in Geometric Aspects of Dwork Theory, edited by A. Adolphson, F. Baldassarri, P. Berthelot, N. Katz and F. Loeser, volume 1, de Gruyter, 509-526 (2004).

J. Denef and F. Vercauteren, An extension of Kedlaya’s algorithm to Artin-Schreier curves in characteristic 2. In C. Fieker and D.R. Kohel, editors, Algorithmic number theory. 5^th international symposium. ANTS-V, volume 2369 of Lecture Notes in Computer Science, pages 308-323. Springer-Verlag Berlin, 2002.

J. Denef and F. Loeser, Motivic integration and the Grothendieck group of pseudo-finite fields, Proceedings of the International Congress of Mathematicians (ICM 2002), Beijing 2002, Volume 2, 13-23, Higher Education Press, Beijing 2002.

J. Denef and F. Loeser, Macdonald integrals and monodromy, International Journal of Mathematics 12 (2001), 987-1004.

J. Denef and S. Sperber, Exponential sums mod p^n and Newton polyhedra. A tribute to Maurice Boffa, Bulletin of the Belgian Mathematical Society --Simon Stevin 2001, suppl., 55-63.

J. Denef, J. Van Geel, L. Lipshitz, and T. Pheidas, editors: Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry, Contemporary Mathematics, 270 (2000), 367 pp. This is the proceedings of a conference at the University of Gent, November 2-5, 1999.

J. Denef and H. Schoutens, On the decidability of the existential theory of F_p[[t]], Valuation Theory and its Applications, Volume II, ed. F.-V. Kuhlmann, S. Kuhlmann and M. Marshall, Fields Institute Communications 33, American Mathematical Society 2003, pp. 43-60.

J. Denef and F. Loeser, Geometry on arc spaces of algebraic varieties, European Congress of Mathematics, Vol. 1 (Barcelona, 2000), 327-348, Progr. Math., 201, Birkhäuser, Basel, 2001.

J. Denef and K. Hoornaert, Newton polyhedra and Igusa’s local zeta function, Journal of Number Theory 89 (2001), 31-64.

J. Denef and F. Loeser, Lefschetz numbers of iterates of the monodromy and truncated arcs, Topology 41 (2002), 1031-1040.

J. Denef and F. Loeser, Definable sets, motives and p-adic integrals, Journal of the American Mathematical Society 14 (2001), 429-469.

J. Denef and F. Loeser, Motivic integration, quotient singularities and the McKay correspondence, Compositio Math. 131 (2002), 267-290.

J. Denef and F. Loeser, Motivic exponential integrals and a motivic Thom-Sebastiani Theorem, Duke Mathematical Journal 99 (1999), 285-309.

J. Denef, Arithmetic and Geometric Applications of Quantifier Elimination for Valued Fields, Model Theory, Algebra, and Geometry, ed. D. Haskell ,A. Pillay, and C. Steinhorn, Cambridge University Press, Math. Sci. Res. Inst. Publ. 39 (2000),173-198. (See also the errata.)

J. Denef and P. Jacobs, On the vanishing of Principal Value Integrals, Comptes Rendus de l' Académie des Sciences de Paris 326 (1998), 1041-1046.

J. Denef, A. Laeremans and P. Sargos, On the largest nontrivial pole of the distribution |f|^s, RIMS Kokyuroku 999 (1997), 1-9.

J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Inventiones Mathematicae 135 (1999), 201-232.

J. Denef and F. Loeser, Motivic Igusa zeta functions, Journal of Algebraic Geometry 7 (1998), 505-537.

J. Denef and F. Loeser, Character sums associated to finite Coxeter groups, Trans. Amer. Math. Soc. 350 (1998), 5047-5066.

J. Denef and A. Gyoja, Character sums associated to prehomogeneous vector spaces, Compositio Math. 113 (1998), 273-346 .

J. Denef, Poles of p-adic Complex Powers and Newton Polyhedra, Nieuw Archief voor Wiskunde (4), 13 (1995), 289-295.

J. Denef and W. Veys, On the holomorphy conjecture for Igusa's local zeta function, Proc. Amer. Math. Soc., 123 (1995), 2981-2988.

J. Denef and F. Loeser, Regular elements and monodromy of discriminants of finite reflection groups, Indagationes Math. (N.S.) 6 (1995), 129-143.

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Electronic versions of some older publications

J. Denef, Report on Igusa's Local Zeta Function, Séminaire Bourbaki 43 (1990-1991), exp. 741; Astérisque 201-202-203 (1991), 359-386.

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Complete publication list till 1994

Publications of Jan Denef from 1974 till 1994

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Remarks to some of my papers

Click here for the remarks

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Slides of some of my lectures

My lecture at Oxford, February 17, 2011: Geometric proofs of theorems of Ax-Kochen and Eršov.

My lecture at the International Congress of Mathematicians (ICM 2002), Beijing 2002: Motivic integration and the Grothendieck group of pseudo-finite fields

My lectures at the Newton Institute for Mathematical Sciences, August 2000: Geometry On Arc Spaces

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Software developed under my direction

POLYGUSA: A computer program to calculate Igusa’s local zeta function and the topological zeta functions of a polynomial that is nondegenerate with respect to its Newton polyhedron. The program is written in Maple V 5.1 for Windows and was developed by K. Hoornaert and D. Loots, under my supervision.

LogicPalet: A computer program designed to help students master the basic concepts of mathematical logic, with emphasis on the semantic aspects of it. It is written by Jan Denef.

Software to calculate zeta functions of hyperelliptic curves over large finite fields. Both the mathematics and software is developed by H. Hubrechts.

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Ph.D. theses under my direction

Ph.Jacobs (1998), A. Laeremans (1997), H. Schoutens (1991), W.Veys (1991), L.Lauwers(1990), J.Pas(1989), D.Bollaerts(1988), A. Herremans (2001), K. Hoornaert (2002), R. Cluckers (2002), F.Vercauteren (2003), J. Nicaise (2004), W. Castryck (2006), H. Hubrechts (2007), J. Tuitman (2011).