Aise Johan de Jong

Last updated

Aise Johan de Jong
Aise Johan de Jong.jpg
De Jong at Oberwolfach, 2004
Born (1966-01-30) 30 January 1966 (age 58)
NationalityDutch
Alma mater Radboud University Nijmegen
Leiden University
Known for Alterations
Stacks Project
Awards Cole Prize (2000)
EMS Prize (1996)
Scientific career
FieldsMathematics
Institutions Columbia University
Massachusetts Institute of Technology
Princeton University
Harvard University
Max Planck Institute for Mathematics
Doctoral advisor Frans Oort
Joseph H. M. Steenbrink
Doctoral students Bhargav Bhatt
Kiran Kedlaya

Aise Johan de Jong (born 30 January 1966) [1] is a Dutch mathematician and professor of mathematics at Columbia University. His research interests include arithmetic geometry and algebraic geometry. He maintains the Stacks Project.

Contents

Early life and education

De Jong was born in Bruges, Belgium on 30 January 1966. [1] He attended the Christelijk Gymnasium Sorghvliet in The Hague, Netherlands. [1] He obtained his master's degree at Leiden University in 1987, under the supervision of Antonius Van de Ven. [1] He earned his Ph.D. cum laude at the Radboud University Nijmegen in 1992, under the supervision of Frans Oort and Joseph H. M. Steenbrink. [1] [2]

Career

De Jong spent 1 year as a visitor at the Max Planck Institute for Mathematics, 3 months as a visitor at Bielefeld University, and then 3 years as a fellow at the Royal Netherlands Academy of Arts and Sciences stationed at Utrecht University. [1] [3] He was a Benjamin Peirce Assistant Professor at Harvard University from 1995 to 1996. [3] He was a professor of mathematics at Princeton University from 1996 to 1998 and then worked at the Massachusetts Institute of Technology from 1998 to 2005. [3] He moved to Columbia University as a professor of mathematics in 2005. [3]

Work

In 1996, de Jong developed his theory of alterations which was used by Fedor Bogomolov and Tony Pantev (1996) and Dan Abramovich and de Jong (1997) to prove resolution of singularities in characteristic 0 and to prove a weaker result for varieties of all dimensions in characteristic p which is strong enough to act as a substitute for resolution for many purposes. [4] [5] [6]

In 2005, de Jong started the Stacks Project, "an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define them." [7] The book that the project has generated currently runs to more than 7500 pages as of July 2022. [8]

Awards and honors

In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. [9] He won the Cole Prize in 2000 for his theory of alterations. [1] In the same year, De Jong became a correspondent of the Royal Netherlands Academy of Arts and Sciences. [10] In 2022 he received the Leroy P. Steele Prize for Mathematical Exposition. [3]

Personal life

De Jong lives in New York City with his wife, Cathy O'Neil, and their three sons. [11]

Selected works

Related Research Articles

<span class="mw-page-title-main">Yuri Manin</span> Russian mathematician (1937–2023)

Yuri Ivanovich Manin was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.

<span class="mw-page-title-main">Shou-Wu Zhang</span> Chinese-American mathematician (born 1962)

Shou-Wu Zhang is a Chinese-American mathematician known for his work in number theory and arithmetic geometry. He is currently a Professor of Mathematics at Princeton University.

Hiraku Nakajima is a Japanese mathematician, and a professor of the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo. He is International Mathematical Union president for the 2023–2026 term.

John Willard Morgan is an American mathematician known for his contributions to topology and geometry. He is a Professor Emeritus at Columbia University and a member of the Simons Center for Geometry and Physics at Stony Brook University.

<span class="mw-page-title-main">Resolution of singularities</span>

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map WV. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem.

In mathematics, the Bogomolov conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin-Mumford conjecture in arithmetic geometry. The conjecture was proven by Emmanuel Ullmo and Shou-Wu Zhang in 1998 using Arakelov theory. A further generalization to general abelian varieties was also proved by Zhang in 1998.

In algebraic geometry, a variety over a field k is ruled if it is birational to the product of the projective line with some variety over k. A variety is uniruled if it is covered by a family of rational curves. The concept arose from the ruled surfaces of 19th-century geometry, meaning surfaces in affine space or projective space which are covered by lines. Uniruled varieties can be considered to be relatively simple among all varieties, although there are many of them.

Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them.

<span class="mw-page-title-main">Kai Behrend</span> German mathematician

Kai Behrend is a German mathematician. He is a professor at the University of British Columbia in Vancouver, British Columbia, Canada.

<span class="mw-page-title-main">William Messing</span> American mathematician

William Messing is an American mathematician who works in the field of arithmetic algebraic geometry.

In commutative algebra and algebraic geometry, Popescu's theorem, introduced by Dorin Popescu, states:

The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them". As of July 2022, the book consists of 115 chapters spreading over 7500 pages. The maintainer of the project, who reviews and accepts the changes, is Aise Johan de Jong.

<span class="mw-page-title-main">Victor Batyrev</span> Russian mathematician

Victor Vadimovich Batyrev is a Russian mathematician, specializing in algebraic and arithmetic geometry and its applications to mathematical physics. He is a professor at the University of Tübingen.

Carlos Tschudi Simpson is an American mathematician, specializing in algebraic geometry.

<span class="mw-page-title-main">Mark Lee Green</span> American mathematician

Mark Lee Green is an American mathematician, who does research in commutative algebra, algebraic geometry, Hodge theory, differential geometry, and the theory of several complex variables. He is known for Green's Conjecture on syzygies of canonical curves.

<span class="mw-page-title-main">Emmanuel Ullmo</span> French mathematician

Emmanuel Ullmo is a French mathematician, specialised in arithmetic geometry. Since 2013 he has served as director of the Institut des Hautes Études scientifiques.

<span class="mw-page-title-main">Frans Oort</span> Dutch mathematician

Frans Oort is a Dutch mathematician who specializes in algebraic geometry.

<span class="mw-page-title-main">Joseph H. M. Steenbrink</span> Dutch mathematician

Joseph Henri Maria Steenbrink is a Dutch mathematician, specializing in algebraic geometry.

Ronald Alan Fintushel is an American mathematician, specializing in low-dimensional geometric topology and the mathematics of gauge theory.

<span class="mw-page-title-main">Bhargav Bhatt (mathematician)</span> Indian-American mathematician

Bhargav Bhatt is an Indian-American mathematician who is the Fernholz Joint Professor at the Institute for Advanced Study and Princeton University and works in arithmetic geometry and commutative algebra.

References

  1. 1 2 3 4 5 6 7 8 "2000 Cole Prize" (PDF). Notices of the American Mathematical Society . 47 (4): 481–482. 2000.
  2. Aise Johan de Jong at the Mathematics Genealogy Project
  3. 1 2 3 4 5 "Aise Johan de Jong receives 2022 Steele Prize for Mathematical Exposition". American Mathematical Society . 9 December 2021. Retrieved 7 March 2024.
  4. de Jong, A. J. (1996), "Smoothness, semi-stability and alterations", Inst. Hautes Études Sci. Publ. Math., 83: 51–93, doi:10.1007/BF02698644, S2CID   53581802
  5. Bogomolov, Fedor A.; Pantev, Tony G. (1996), "Weak Hironaka theorem", Mathematical Research Letters, 3 (3): 299–307, arXiv: alg-geom/9603019 , Bibcode:1996alg.geom..3019B, doi:10.4310/mrl.1996.v3.n3.a1, S2CID   14010069
  6. Abramovich, D; de Jong, A. J. (1997), "Smoothness, semistability, and toroidal geometry", Journal of Algebraic Geometry, 6 (4): 789–801, arXiv: alg-geom/9603018 , Bibcode:1996alg.geom..3018A, MR   1487237
  7. "The Stacks Project » About". columbia.edu . Retrieved 30 August 2013.
  8. Johan de Jong; et al. The Stacks Project (PDF). Retrieved 29 January 2017.
  9. de Jong, A. J. (1998). "Barsotti-Tate groups and crystals". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 259–265.
  10. "Aise de Jong". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 14 October 2018. Retrieved 4 August 2015.
  11. "mathbabe.org about page". 11 June 2011. Retrieved 25 July 2013.