# General Information

Professor at the University of Leuven (KU Leuven), Doctor Honoris Causa of Ovidius University of Constanța, Department of Mathematics, Section of Algebra.

wim.veys (at) kuleuven.be

#### Fields of Research

Algebraic Geometry, Singularity Theory, Applications in Number Theory.

#### Specific Research topics

• Exceptional divisor of an embedded resolution,
• Zeta Functions (Igusa, topological, motivic),
• Monodromy,
• Configurations of curves on surfaces,
• Surface singularities,
• Stringy invariants,
• Principal value integrals,
• Newton trees,
• Exponential sums, Kloosterman sums,
• Divisorial valuations.

#### Co-authors

Hans Baumers, Bart Bories, Pierrette Cassou-Noguès, Thomas Cauwbergs, Raf Cluckers, Evi Daems, Jan Denef, Ke Gong, Arno Kuijlaars, Ann Laeremans, Ann Lemahieu, Edwin León-Cardenal, Alejandro Melle, András Némethi, Bart Rodrigues, Jan Schepers, Dirk Segers, Tristan Torrelli, Leen Van Langenhoven, Lise Van Proeyen, Daqing Wan, Wilson Zúñiga-Galindo.

University of Leuven Department of Mathematics Celestijnenlaan 200B B-3001 Leuven (Heverlee) Belgium

(+32)16-327092

(+32)16-327998

# Ph.D. Students

Dr. Bart Rodrigues: Geometric determination of the poles of motivic and topological zeta functions, May 2002.
Dr. Dirk Segers: Smallest poles of Igusa's and topological zeta functions and solutions of polynomial congruences, April 2004.
Dr. Jan Schepers: Stringy invariants of singular algebraic varieties, May 2006.
Dr. Ann Lemahieu (other advisor: Antonio Campillo, Univ. Valladolid): Poincaré series and zeta functions, March 2007.
Dr. Filip Cools (other advisor: Marc Coppens): Grassmann secant varieties and plane curves with total inflection points, May 2007.
Dr. Lise Van Proeyen: Local zeta functions for ideals and the monodromy conjecture, July 2008.
Dr. Tim Wouters (other advisor: Philippe Gille, Paris): Cohomological approach of obstructions for the existence of rational points, May 2010.
Dr. Bart Bories: Zeta functions, Bernstein-Sato polynomials, and the monodromy conjecture, April 2013.
Dr. Leen Van Langenhoven: Semigroup and Poincaré series for divisorial valuations, October 2013.
Dr. Ferran Dachs-Cadefau (other advisor: Josep Alvarez, Maria Alberich): Multiplier ideals in two-dimensional local rings with rational singularities, June 2016.
Dr. Thomas Cauwbergs (other advisor: Johannes Nicaise): Motivic Zeta Functions, Splicing and the Milnor Fibration, July 2016.
Dr. Marta Panizzut (other advisor: Filip Cools, Marc Coppens): Linear systems on metric graphs, gonality and lifting problems, October 2016.
Dr. Hans Baumers: Jumping numbers in higher dimensions: computation and contribution by exceptional divisors, October 2016.
Jasper Van Hirtum (other advisor: Gabor Wiese, Jan Tuitman): Computation and asymptotics of coefficients of modular forms.
Lena Vos: The monodromy conjecture for ideals.

# Publications

Available with PDF() and/or PS() starting from 1992.
Monodromy eigenvalues and poles of zeta functions
and , Bulletin of the London Mathematical society, (to appear), 10p.
Contribution of jumping numbers by exceptional divisors
and , preprint, (2016), 21p.
Power moments of Kloosterman sums
, and , Journal of Number Theory, 164, (2016), 103-126.
Igusa's p-adic local zeta function and the monodromy conjecture for non-degenerated surface singularities
and , Memoirs of the American Mathematical Society, 242, 1145, (2016), vii+131pp.
Bounds for $$p$$-adic exponential sums and log-canonical thresholds
and , American Journal of Mathematics, 138, 1, (2016), 61-80.
Zeta functions and oscillatory integrals for meromorphic functions
and , Advances in Mathematics, (to appear), 36p.
The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold
and , Mathematical Proceedings of the Cambridge Philosophical Society, 159, (2015), 481-515.
Semigroup and Poincaré series for a finite set of divisorial valuations
and , Revista Matematica Complutense, 28, 1, (2015), 191-225.
Newton trees for ideals in two variables and applications
and , Proceedings of the London Mathematical Society, 108, 4, (2014), 869-910.
Bridging Algebra, Geometry, and Topology. Proceedings of "Experimental and Theoretical Methods in Algebra, Geometry and Topology", Eforie Nord, Romania, June 21-24, 2013
and , Springer Proceedings in Mathematics & Statistics, 96, (2014), xii+289 pp.
Poles of Archimedean zeta functions for analytic mappings
, and , Journal of the London Mathematical Society, 87, (2013), 1-21.
Zeta functions in algebra and geometry, Papers from the 2nd International Workshop held at the Universitat de les Illes Balears, Palma de Mallorca, May 3-7, 2010
, , , and , Contemporary Mathematics, 566. American Mathematical Society, Providence, RI; Real Sociedad Matemática Española, Madrid, (2012), xvi+344 pp.
Generalized monodromy conjecture in dimension two
and , Geometry & Topology, 16, (2012), 155-217.
On the local zeta functions and b-functions of certain hyperplane arrangements
, and , With an appendix by W. Veys, Journal of the London Mathematical Society, 84, 2, (2011), 631-648.
Monodromy Jordan blocks, b-functions and poles of zeta functions for germs of plane curves
, and , Journal of Algebra, 324, 6, (2010), 1364-1382.
Monodromy eigenvalues are induced by poles of zeta functions: the irreducible curve case
and , The Bulletin of the London Mathematical Society, 42, 2, (2010), 312-322.
The Monodromy Conjecture for zeta functions associated to ideals in dimension two
and , Annales de l'Institut Fourier, 60, 4, (2010), 1347-1362.
On 'maximal' poles of zeta functions, roots of b-functions, and monodromy Jordan blocks
, and , Journal of Topology, 2, 3, (2009), 517-526.
Stringy E-functions of hypersurfaces and of Brieskorn singularities
and , Advances in Geometry, 9, 2, (2009), 199-217.
Zeta functions and monodromy for surfaces that are general for a toric idealistic cluster
and , International Mathematics Research Notices, 1, (2009), 11-62.
Poles of the topological zeta function associated to an ideal in dimension two
and , Mathematische Zeitschrift, 260, 3, (2008), 615-627.
Asymptotics of non-intersecting Brownian motions and a 4x4 Riemann-Hilbert problem
, and , Journal of Approximation Theory, 153, 2, (2008), 225-256.
Zeta functions for polynomial mappings, log-principalization of ideals, and Newton polyhedra
and , Transactions of the American Mathematical Society, 360, (2008), 2205-2227.
Stringy Hodge numbers for a class of isolated singularities and for threefolds
and , International Mathematics Research Notices, (2007), ID rnm016.
On monodromy for a class of surfaces
and , Comptes Rendus de l'Académie des Sciences. Série I, Mathématique, 345, (2007), 633-638.
The motivic zeta function and its smallest poles
, and , Journal of Algebra, 317, (2007), 851-866.
On motivic principal value integrals
, Mathematical Proceedings of the Cambridge Philosophical Society, 143, (2007), 543-555.
Monodromy eigenvalues and zeta functions with differential forms
, Advances in Mathematics, 213, (2007), 341-357.
On the poles of topological zeta functions
, and , Proceedings of the American Mathematical Society, 134, 12, (2006), 3429-3436.
Vanishing of principal value integrals on surfaces
, Journal fur die Reine und Angewandte Mathematik, 598, (2006), 139-158.
Arc spaces, motivic integration and stringy invariants
, Izumiya, S. et al. (Ed.), Advanced Studies in Pure Mathematics 43, Singularity theory and its applications, Sapporo, 16-25 September 2003, (2006), 529-572, Tokyo, Mathematical Society of Japan.
Stringy invariants of normal surfaces
, Journal of Algebraic Geometry, 13, 1, (2004), 115-141.
On the smallest poles of topological zeta functions
and , Compositio Mathematica, 140, 1, (2004), 130-144.
Stringy zeta functions for $$\mathbb{Q}$$-Gorenstein varieties
, Duke Mathematical Journal, 120, 3, (2003), 469-514.
Poles of zeta functions on normal surfaces
and , Proceedings of the London Mathematical Society, 87, (2003), 164-196.
Holomorphy of Igusa's and topological zeta functions for homogeneous polynomials
and , Pacific Journal of Mathematics, 201, 2, (2001), 429-440.
Zeta functions and 'Kontsevich invariants' on singular varieties
, Canadian Journal of Mathematics-Journal Canadien de Mathématiques, 53, 4, (2001), 834-865.
Embedded resolution of singularities and Igusa's local zeta function
, Academiae Analecta: Mededelingen van de Koninklijke Academie voor Wetenschappen, Letteren, (2001), 1-56.
The topological zeta function associated to a function on a normal surface germ
, Topology, 38, 2, (1999), 439-456.
On the poles of maximal order of the topological zeta function
and , Bulletin of the London Mathematical Society, 31, (1999), 441-449.
More congruences for numerical data of an embedded resolution
, Compositio Mathematica, 112, 3, (1998), 313-331.
Structure of rational open surfaces with non-positive Euler characteristic
, Mathematische Annalen, 312, 3, (1998), 527-548.
Zeta functions for curves and log canonical models
, Proceedings of the London Mathematical Society, 74, (1997), 360-378.
On Euler characteristics associated to exceptional divisors
, Transactions of the American Mathematical Society, 347, 9, (1995), 3287-3300.
Determination of the poles of the topological zeta function for curves
, Manuscripta Mathematica, 87, 4, (1995), 435-448.
On the holomorphy conjecture for Igusa's local zeta function
and , Proceedings of the American Mathematical Society, 123, 10, (1995), 2981-2988.
Holomorphy of local zeta functions for curves
, Mathematische Annalen, 295, 4, (1993), 635-641.
Poles of Igusa's local zeta function and monodromy
, Bulletin de la Société Mathématique de France, 121, 4, (1993), 545-598.
Reduction modulo $$p^n$$ of $$p$$-adic subanalytic sets
, Mathematical Proceedings of the Cambridge Philosophical Society, 112, (1992), 483-486.
Congruences for numerical data of an embedded resolution
, Compositio Mathematica, 80, 2, (1991), 151-169.
Relations between numerical data of an embedded resolution
, American Journal of Mathematics, 113, 4, (1991), 573-592.
Relations between numerical data of an embedded resolution
, Astérisque, 198, (1991), 397-403.
On the poles of Igusa's local zeta function for curves
, Journal of the London Mathematical Society-second series, 41, (1990), 27-32.
On the poles of local zeta functions for curves
, Bueso, J. et al. (Ed.), Proceedings of the 1st Belgian-Spanish week on Algebra and Geometry, Belgian-Spanish week on Algebra and Geometry, Antwerpen, 8-15 July 1988, (1988), 173-181.
Last revised: January 2017
Design and coding by Thomas Cauwbergs