Aise Johan de Jong

Aise Johan de Jong
Name	Aise Johan de Jong
Birth date	1966
Birth place	Amsterdam
Nationality	Dutch
Fields	Mathematics
Workplaces	Columbia University, University of Michigan, Princeton University, Cornell University, Massachusetts Institute of Technology
Alma mater	Leiden University, University of California, Berkeley
Doctoral advisor	Joost van Hamel
Known for	algebraic geometry, stacks, de Jong alterations
Awards	Cole Prize, Royal Netherlands Academy of Arts and Sciences

Aise Johan de Jong is a Dutch mathematician noted for foundational work in algebraic geometry, arithmetic geometry, and the theory of stacks. He introduced techniques that reshaped approaches to resolution problems, moduli, and cohomological methods, influencing researchers across Harvard University, Yale University, Princeton University, University of Cambridge, and École Normale Supérieure. His contributions connect to problems studied by mathematicians at institutions such as Institute for Advanced Study, Max Planck Institute for Mathematics, IHÉS, and University of Chicago.

Early life and education

Born in Amsterdam in 1966, de Jong studied at Leiden University where he completed undergraduate work interacting with scholars from University of Utrecht and Radboud University Nijmegen. He pursued graduate studies at University of California, Berkeley under influences from faculty associated with Stanford University and University of California, Los Angeles. During his doctoral training he encountered ideas from researchers at Princeton University and collaborators linked to ETH Zurich and University of Bonn, shaping his focus on problems originating in the tradition of Alexander Grothendieck, Jean-Pierre Serre, and Pierre Deligne.

Academic career and positions

De Jong held appointments and visiting positions across prominent centers including faculty posts at Columbia University, visiting positions at Institute for Advanced Study, and collaborations with groups at University of Michigan, Cornell University, and Massachusetts Institute of Technology. He has spoken at major gatherings such as the International Congress of Mathematicians, the European Mathematical Congress, and workshops at Mathematical Sciences Research Institute and Banff International Research Station. His interactions span networks including researchers from Princeton University, Harvard University, Yale University, University of Cambridge, University of Oxford, and the Max Planck Institute for Mathematics.

Contributions to algebraic geometry

De Jong developed the theory of alterations, a flexible substitute for resolution of singularities, which influenced directions at IHÉS, ENS Lyon, Université Paris-Sud, and the University of Warwick. His work on stacks and moduli complements frameworks advanced at Institut des Hautes Études Scientifiques and by mathematicians at University of California, Berkeley, Columbia University, Stanford University, and Harvard University. He advanced methods applicable to the study of étale cohomology, l-adic cohomology, and crystalline cohomology, linking to research by Pierre Deligne, Grothendieck, Nicholas Katz, and Luc Illusie. His techniques have been applied to problems investigated at University of Bonn, Hamburg University, University of Tokyo, Kyoto University, and Seoul National University.

Major results and conjectures

The de Jong alterations theorem provided a tool paralleling efforts by Hironaka and later researchers at University of California, Berkeley and Princeton University tackling resolution in positive characteristic. He formulated and proved results impacting the Brauer group and period-index problems studied by scholars at ETH Zurich, University of Chicago, Columbia University, and University of Cambridge. His approaches influenced proofs and conjectures connected to work by Jean-Louis Colliot-Thélène, Bjorn Poonen, Max Lieblich, Brian Conrad, and Martin Olsson. De Jong's techniques have been instrumental for progress on questions related to moduli of vector bundles, Gromov–Witten theory as developed at UC San Diego and Princeton University, and arithmetic applications pursued at Courant Institute, Rutgers University, and University of Arizona.

Awards and honors

De Jong received recognition from national and international bodies including membership in the Royal Netherlands Academy of Arts and Sciences and prizes akin to the Cole Prize in recognition of his impact on algebraic geometry. He has been invited to give plenary and invited lectures at forums such as the International Congress of Mathematicians, the European Mathematical Society, and key symposia at Mathematical Sciences Research Institute and Banff International Research Station. His influence is cited in work by recipients of awards from institutions like American Mathematical Society, Clay Mathematics Institute, Simons Foundation, and German Research Foundation.

Selected publications and legacy

De Jong's seminal paper introducing alterations and subsequent expositions on stacks and moduli are widely cited across literature emerging from Princeton University Press, Springer-Verlag, Cambridge University Press, and journals such as the Annals of Mathematics, Journal of the American Mathematical Society, Inventiones Mathematicae, and Duke Mathematical Journal. His methods continue to inform research at Institute for Advanced Study, Mathematical Sciences Research Institute, Max Planck Institute for Mathematics, IHÉS, and universities including Harvard University, Yale University, University of Cambridge, and University of Oxford. Students and collaborators from Columbia University, University of Michigan, Cornell University, and MIT have extended his approaches to contemporary problems in algebraic and arithmetic geometry, ensuring a lasting legacy across the global mathematical community.

Category:Dutch mathematicians Category:Algebraic geometers