Sebastiaan Johan Edixhoven (12 March 1962 – 16 January 2022) was a Dutch mathematician who worked in

arithmetic geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

. He was a professor at University of Rennes 1 and Leiden University.

Education

Bas Edixhoven was born on 12 March 1962 in

Leiden Leiden (; in English and archaic Dutch also Leyden) is a city and municipality in the province of South Holland, Netherlands. The municipality of Leiden has a population of 119,713, but the city forms one densely connected agglomeration wit ...

, Netherlands. Edixhoven graduated from in

Zoetermeer Zoetermeer () is a city in the Western Netherlands, in the province of South Holland. The municipality covers an area of of which is water. A small village until the late 1960s, it had 6,392 inhabitants in 1950. By 2013 this had grown to 123,328 ...

in 1980. He then studied at

Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public research university in Utrecht, Netherlands. Established , it is one of the oldest universities in the Netherlands. In 2018, it had an enrollm ...

where he graduated with a master's degree in pure mathematics ''

cum laude Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some So ...

'' in 1985 and a PhD in mathematics in 1989, both under the direction of Frans Oort. His thesis was about

modular curve In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular ...

Career

Edixhoven was a Morrey assistant professor at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

from 1989 to 1991, after which he returned to Utrecht University. From 1992 to 2002, he was a professor at the University of Rennes 1. He moved to Leiden University as a Professor of Geometry in 2002. In 2004, Edixhoven and Peter Stevenhagen established Leiden's participation in the Algebra, Geometry and Number Theory (ALGANT) collaborative program for master's and PhD students across French, Italian, German, Canadian, and Dutch universities. Edixhoven was a co-managing editor of ''

Compositio Mathematica ''Compositio Mathematica'' is a monthly peer-reviewed mathematics journal established by L.E.J. Brouwer in 1935. It is owned by the Foundation Compositio Mathematica, and since 2004 it has been published on behalf of the Foundation by the London ...

'' from 2003 to 2012. He was an editor for ''Compositio Mathematica'' from 2000 to 2012, for the '' Journal de Théorie des Nombres de Bordeaux'' from 1998 to 2004, for the '' Journal of Number Theory'' from 2004 to 2012, for '' Expositiones Mathematicae'' from 2003 to 2022, and for ''

Indagationes Mathematicae ''Indagationes Mathematicae'' (from Latin: ''inquiry, search, investigation of the mathematics'') is a Dutch mathematics journal. The journal originates from the ''Proceedings of the Royal Netherlands Academy of Arts and Sciences'' (or ''Proc ...

'' from 2010 to 2022. Edixhoven was involved in the Bèta-lerarenkamer think tank, which produced a mobile app for refugee teachers to improve their Dutch and mathematics abilities.

Research

Edixhoven's early work was on modular curves. He worked on the techniques used in

Wiles's proof of Fermat's Last Theorem Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Ferma ...

and the proof of Serre's modularity conjecture. He later made important contributions regarding the

André–Oort conjecture In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem (and is actually proven in several g ...

, as well as making

modular forms In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of ...

and associated

Galois representations In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring i ...

more computationally accessible. His latest works had focused on geometric interpretations of the quadratic

Chabauty method This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of pro ...

. Outside of academia, he worked on correction codes for the French Ministry of Defense and Canon Inc.

Awards

From 1989 to 1992, Edixhoven was a recipient of the Huygens scholarship. From 1995 to 2002, he was a member of the

Institut Universitaire de France The Institut Universitaire de France (IUF, Academic Institute of France), is a service of the French Ministry of Higher Education that distinguishes each year a small number of university professors for their research excellence, as evidenced by t ...

. In 2009, he became a member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

. In 2008, he gave an invited lecture at the 5th

European Congress of Mathematics The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses of Mathematicians (ICM). The ECM are held every four years and are timed precisely betwee ...

Death

Edixhoven died on 16 January 2022, at the age of 59, from a

tumor A neoplasm () is a type of abnormal and excessive growth of tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tissue, and persists ...

Selected publications

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References

{{DEFAULTSORT:Edixhoven, Bas 1962 births 2022 deaths 20th-century Dutch mathematicians 21st-century Dutch mathematicians Academic staff of Leiden University Dutch academics Members of the Royal Netherlands Academy of Arts and Sciences University of California, Berkeley faculty