Hendrik Lenstra

{{Infobox scientist

| name = Hendrik Lenstra

| image = Hendrik Lenstra MFO.jpg

| image_size = 250px

| caption = Hendrik W. Lenstra Jr.

| birth_date = {{Birth date and age|1949|04|16|df=y}}

| birth_place = Zaandam, Netherlands

| death_date =

| death_place =

| nationality = Dutch

| fields = Mathematics

| workplaces = University of California, Berkeley
University of Leiden

| alma_mater = University of Amsterdam

| doctoral_advisor = Frans Oort

| thesis_title = Euclidische getallenlichamen

| thesis_year = 1977

| doctoral_students = {{plainlist|

}}

| known_for = Lenstra elliptic-curve factorization
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Pomerance–Wagstaff conjecture
APR-CL primarily test

| awards = {{plainlist|

Fulkerson Prize (1985)
Spinoza Prize (1988)
Gauss Lecture (2009)
American Mathematical Society Fellow (2012)

}}

Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician.

Biography

Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987, he was appointed to the faculty of the University of California, Berkeley; starting in 1998, he divided his time between Berkeley and the University of Leiden, until 2003, when he retired from Berkeley to take a full-time position at Leiden.[http://albumacademicum.uva.nl/id/id001147 Prof. dr. H.W. Lenstra, 1949 -] at the University of Amsterdam Album Academicum website

Three of his brothers, Arjen Lenstra, Andries Lenstra, and Jan Karel Lenstra, are also mathematicians. Jan Karel Lenstra is the former director of the Netherlands Centrum Wiskunde & Informatica (CWI). Hendrik Lenstra was the Chairman of the Program Committee of the International Congress of Mathematicians in 2010.[http://www.mathunion.org/activities/icm ICM – International Congress of Mathematicians]

Scientific contributions

Lenstra has worked principally in computational number theory. He is well known for:

Co-discovering of the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982);
Developing an polynomial-time algorithm for solving a feasibility integer programming problem when the number of variables is fixed (in 1983);H.W. Lenstra, "Integer programming with a fixed number of variables", Mathematics of operations research, Vol 8, No 8, November 1983
Discovering the elliptic curve factorization method (in 1987);Factoring integers with elliptic curves. Annals of Mathematics, vol. 126, 1987, pp. 649–673
Computing all solutions to the inverse Fermat equation (in 1992);{{cite journal|author=Lenstra Jr. H.W.|author-link=Hendrik Lenstra|year=1992|title=On the inverse Fermat equation|journal=Discrete Mathematics|volume=106–107|pages=329–331|doi=10.1016/0012-365x(92)90561-s|doi-access=}}
The Cohen-Lenstra heuristics - a set of precise conjectures about the structure of class groups of quadratic fields.{{citation|last1=Cohen|first1=Henri|title=A Course in Computational Algebraic Number Theory|year=1993|chapter=Chapter 5.10|location=Berlin|publisher=Springer|isbn=978-3-540-55640-4}}

Awards and honors

In 1984, Lenstra became a member of the Royal Netherlands Academy of Arts and Sciences.{{cite web |url=https://www.knaw.nl/en/members/members/4462 |title=Hendrik Lenstra |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=19 July 2015 |archive-date=4 March 2016 |archive-url=https://web.archive.org/web/20160304054658/https://www.knaw.nl/en/members/members/4462 |url-status=dead }} He won the Fulkerson Prize in 1985 for his research using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints.[http://www.mathopt.org/?nav=fulkerson#winners Past winners of the Fulkerson Prize], retrieved 2015-07-18. He was awarded the Spinoza Prize in 1998,{{cite web |url=http://www.nwo.nl/en/research-and-results/programmes/spinoza+prize/spinoza+laureates/overview+by+year/1998 |title=NWO Spinoza Prize 1998 |publisher=Netherlands Organisation for Scientific Research |date=11 September 2014 |access-date=30 January 2016 |archive-date=9 March 2018 |archive-url=https://web.archive.org/web/20180309054532/https://www.nwo.nl/en/research-and-results/programmes/spinoza+prize/spinoza+laureates/overview+by+year/1998 |url-status=dead }} and on 24 April 2009 he was made a Knight of the Order of the Netherlands Lion. In 2009, he was awarded a Gauss Lecture by the German Mathematical Society. In 2012, he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.

Publications

Euclidean Number Fields. Parts 1-3, Mathematical Intelligencer 1980
with A. K. Lenstra: Algorithms in Number Theory. pp. 673–716, In Jan van Leeuwen (ed.): Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity. Elsevier and MIT Press 1990, {{ISBN|0-444-88071-2}}, {{ISBN|0-262-22038-5}}.
[https://www.ams.org/bull/1992-26-02/S0273-0979-1992-00284-7/home.html Algorithms in Algebraic Number Theory.] Bulletin of the AMS, vol. 26, 1992, pp. 211–244.
[https://web.archive.org/web/20140222062213/http://www.numdam.org/numdam-bin/fitem?id=SB_1980-1981__23__243_0 Primality testing algorithms.] Séminaire Bourbaki 1981.
with Peter Stevenhagen: [http://www.math.leidenuniv.nl/~naw/serie5/index.php?deel=1&nummer=1&taal=1 Artin reciprocity and Mersenne Primes.] Nieuw Archief for Wiskunde 2000.
with Peter Stevenhagen: Chebotarev and his density theorem. Mathematical Intelligencer 1992 (Online at Lenstra's Homepage).
[http://www.math.leidenuniv.nl/~hwl/papers/fibo.pdf Profinite Fibonacci Numbers, December 2005, PDF]