Jan-Hendrik Evertse

Curriculum vitae

Mathematical Institute |  JHE's homepage

Personal: Date and place of birth: May 13, 1958, Rotterdam (Netherlands)
Present citizenship: Dutch
Citizenship at birth: Dutch
Family status: Unmarried
Affiliation: Universiteit Leiden
Mathematisch Instituut
Postbus 9512, 2300 RA Leiden
The Netherlands
Present position: Universitair docent (assistant professor)
Graduation: September 28, 1979 (Universiteit Leiden)
Defense Ph-D. thesis: September 7, 1983 (Universiteit Leiden)

Supervisor:  Prof. dr. R. Tijdeman
2nd supervisor:  Prof. dr. F. Beukers
Title of dissertation:  Upper bounds for the numbers of solutions of Diophantine equations (published at CWI, Amsterdam)

Research area: Number theory.
In particular Diophantine approximations, finiteness problems for the number of solutions of Diophantine equations and Diophantine inequalities, and estimates for the number of solutions.
Editorial work: Editor of Compositio Mathematica
Research positions:
1979-1983:Ph-D. student at Universiteit Leiden
1984-1988:Researcher on cryptology at CWI (Centre for Mathematics and Computer Science, Amsterdam)
1988-1993:Fellowship of KNAW (Royal Dutch Academy of Arts and Sciences) for research in number theory at Universiteit Leiden
1993-... :Universitair docent (Assistant professor) at Universiteit Leiden
Foreign visits
for longer periods
(all on invitation):
Sept-Dec 1988:University of Debrecen (inv. Prof. K. Györy)
Jan-Feb 1990:University of Waterloo (Canada) (inv. Prof. C.L. Stewart)
March-Apr 1990:University of Colorado at Boulder (inv. Prof. W.M. Schmidt)
Jan-May 1993:Mathematical Sciences Research Institute (Berkeley)   (special semester on Diophantine approximations)
June 1996: University of Ulm (inv. Prof. H.P. Schlickewei)
Sept-Dec 1997:Institute for Advanced Study (membership)
June 1998: University of Marburg (inv. Prof. H.P. Schlickewei)
Feb 1999: Institut Henri Poincaré (Paris)  (special trimester on Diophantine geometry)
Jan 2001: ETH Zürich (inv. Dr. R. Ferretti)
Jan 2003: University of Debrecen (inv. Prof. K. Györy)
May-June 2005: Centro di Ricerca Matematica Ennio de Giorgi (Pisa)  (special trimester on Diophantine geometry)
Aug 2005: University of Debrecen (inv. Dr. A. Bérczes, Prof. K. Györy)
March 2006: Erwin Schroedinger Institut (Vienna)  (trimester on Diophantine approximation and heights)
Teaching experience: Courses to first and second year mathematics students:
Linear algebra, Algebra (rings), Algebra (fields and Galois theory)

Courses to third and higher years mathematics students:
Basic number theory, Combinatorics, Cryptography, Computational number theory, Algebraic number theory, Diophantine approximation, Analytic number theory

Courses to non-mathematical students:
Calculus, Linear algebra, Algebraic structures to first year computer science students;
Calculus to first year biology students;
Linear algebra to second year students biopharmaceutical sciences;
Calculus to first year Life science and technology students.

Organization and administration: - Member of the program committee of Eurocrypt 1987 (Amsterdam)
- Member of the organization committees of the Dutch Mathematical Conferences 1994, 2006, 2007.
- Writer (together with Jaap van de Griend) of the "zelfstudie t.b.v. de visitatiecommissie onderwijs wiskunde 1996" (report for a Dutch committee investigating the quality of the mathematics curricula at the various Dutch universities)
- Organizer of the workshop "Diophantine approximation" and the symposium in honour of the 60th birthday of Prof. Robert Tijdeman in 2003 (together with Frits Beukers and Pieter Moree)
- Organizer of the instructional conference "Solvability of Diophantine equations" and the workshop "Solvability of Diophantine equations" in 2007 (together with Mike Bennett, Frits Beukers and Rob Tijdeman)
- Organizer of the symposium "Number Theory and Discrete Mathematics" in honour of the 65th birthday of Prof. Robert Tijdeman in 2008 (together with Fred Bakker, Joost Batenburg and Lodewijk Kallenberg)
- Organizer of the General mathematics colloquium in Leiden 1996-2009 (together with Floske Spieksma and Frank Redig)
- Assistant education coordinator for mathematics 2010 -- (class schedules and study guide)
Research experience: From 1979-1983 I worked as a Ph-D student in Leiden, under supervision of Rob Tijdeman and Frits Beukers. The purpose of my Ph-D research was to give as good as possible estimates for the number of solutions of Diophantine equations, using techniques from Diophantine approximation.
From 1984-1988 I worked as a researcher at the CWI in Amsterdam in the cryptography group of David Chaum. There, my research was focused on cryptographic protocols and on the Data Encryption Standard.
In 1988 I went back to Leiden and continued the research I started as a Ph-D student. From 1988-1993 I was a KNAW fellow, and since 1993 a Universitair Docent in the Leiden number theory group. Since then I have been working on Diophantine approximation, Diophantine equations and Diophantine inequalities, in particular on matters such as the Thue-Mahler equation, discriminants and resultants of binary forms, decomposable form equations, S-unit equations, Faltings' Product Theorem, Schmidt's Subspace Theorem, symmetric improvements of Liouville's inequality, approximation of algebraic numbers by algebraic numbers of bounded degree.
My research in the past few years concerns generalizations and refinements of Schmidt's Subspace Theorem, estimating the number of equivalence classes of pairs of binary forms with given resultant, approximation of complex algebraic numbers by algebraic numbers of bounded degree, complexity of expansions of real algebraic numbers with respect to a given base, multiply monogenic orders, effective finiteness results for points from the intersection of a subvariety of a linear torus and a group of finite rank over the algebraic closure of Q, effective results on unit equations over finitely generated domains. I have recently finished a book with Kálmán Györy on unit equations. Kálmán and I are presently working on a second book on Diophantine problems related to discriminants of polynomials and binary forms.
Lectures: List of lectures
Coauthors: Papers on number theory:
A. Bérczes, B. Brindza, Y. Bugeaud, C. Pontreau, R.G. Ferretti, I. Gaál, K. Györy, N. Hirata-Kohno, P.Moree, H.P. Schlickewei, W.M. Schmidt, T.N. Shorey, J.H. Silverman, C.L. Stewart, R. Tijdeman, U. Zannier

Papers on cryptography:
D. Chaum, J. van de Graaf, E. van Heyst, R. Peralta

Main publications:
1.   On equations in S-units and the Thue-Mahler equation, Invent. math. 75 (1984), 561-584.
2. On sums of S-units and linear recurrences, Compos. Math. 53 (1984), 225-244.
3. (with K. Györy, C.L. Stewart and R. Tijdeman), S-unit equations in two unknowns, Invent. math. 92 (1988), 461-477.
4. (with K. Györy) Effective finiteness results for binary forms with given discriminant, Compos. Math. 79 (1991), 169-204.
5. The number of solutions of decomposable form equations, Invent. math. 122 (1995), 559-601.
6. An improvement of the quantitative Subspace Theorem, Compos. Math. 101 (1996), 225-311.
7. Symmetric improvements of Liouville's inequality, J. reine angew. Math. 527 (2000), 69-95.
8. (with R. Ferretti) Diophantine inequalities on projective varieties, Intern. Math. Res. Not. 2002:25 (2002), 1295-1330.
9. (with H.P. Schlickewei, W.M. Schmidt) Linear equations in variables which lie in a multiplicative group, Ann. Math. 155 (2002), 1-30.
10. (with H.P. Schlickewei) A quantitative version of the Absolute Subspace Theorem, J. reine angew. Math. 548 (2002), 21-127.
11. (with R.G. Ferretti) A generalization of the Subspace Theorem with polynomials of higher degree. In: Diophantine Approximation, Festschrift for Wolfgang Schmidt, R.F. Tichy, H.P. Schlickewei, K. Schmidt (eds.), Proceedings of a conference in honour of Prof. Wolfgang Schmidt's 70th birthday, held in Vienna, October 6-10, 2003, Springer Verlag, 2008, pp. 175-198.
12. (with R.G. Ferretti) A further improvement of the Quantitative Subspace Theorem. Annals of Math. 177 (2013), 513-590.
13. (with K. Györy) Unit Equations in Diophantine Number Theory. Cambridge Studies in Advanced Mathematics 146, ISBN 9781107097605, Cambridge University Press, 2015.
List of all publications
Together with Bas Edixhoven I have edited the volume "Diophantine Approximation and Abelian Varieties," Springer LNM 1566, 1993, containing the proceedings of an instructional conference for Ph-D students held in Soesterberg (The Netherlands) from April 12-16, 1992.