János Kollár

János Kollár
Name	János Kollár
Birth date	1956
Birth place	Budapest, Hungary
Nationality	Hungarian
Fields	Algebraic geometry, Complex geometry
Alma mater	Eötvös Loránd University, Brandeis University
Doctoral advisor	Robin Hartshorne
Known for	Minimal model program, Rationally connected varieties
Awards	Cole Prize, AMS, Shaw Prize

János Kollár

János Kollár is a Hungarian mathematician known for foundational work in algebraic geometry, particularly birational geometry, the minimal model program, and the theory of rationally connected varieties. He has held professorships and visiting positions at institutions including Princeton University, Harvard University, University of Utah, and Massachusetts Institute of Technology, and has influenced research directions through monographs, survey articles, and graduate texts. His contributions intersect the work of figures such as Shigefumi Mori, Yakov Eliashberg, Claire Voisin, and Jean-Pierre Serre and have been recognized by awards including the Cole Prize (AMS), the Shaw Prize, and membership in academies like the National Academy of Sciences (United States).

Early life and education

Kollár was born in Budapest and received his early education in Hungary during the Cold War era, a milieu that also produced mathematicians such as Paul Erdős and Peter Lax. He completed undergraduate studies at Eötvös Loránd University and moved to the United States for doctoral study at Brandeis University, where he studied under Robin Hartshorne, joining a lineage linked to Oscar Zariski and André Weil. His dissertation work connected to themes in birational geometry that resonate with the achievements of Enriques–Kodaira classification contributors and the program initiated by Federigo Enriques and Kunihiko Kodaira.

Academic career and positions

Kollár's early postdoctoral appointments included positions at Princeton University and research visits to institutions such as Institute for Advanced Study and IHÉS. He served on the faculty at the University of Utah and later held posts at Massachusetts Institute of Technology before moving to Princeton University and other research centers. He has been a visiting scholar at universities and institutes including Stanford University, Harvard University, University of Cambridge, and École Normale Supérieure, collaborating with contemporaries like Shigefumi Mori, János Bolyai Society affiliates, and researchers connected to the European Mathematical Society. Kollár has supervised doctoral students who continued in fields related to birational geometry, moduli spaces, and complex algebraic varieties and has served on editorial boards of journals such as Journal of the American Mathematical Society and Inventiones Mathematicae.

Research contributions and major results

Kollár's research advanced the minimal model program (MMP) by extending methods for higher-dimensional varieties and contributing to the understanding of flips, flops, and divisorial contractions central to the MMP developed by Shigefumi Mori and Miles Reid. He proved existence and properties of certain flips and applied techniques from Hodge theory and Mori theory to address questions about singularities of pairs, linking to concepts introduced by Vladimir Voevodsky and Masayoshi Nagata. Kollár co-developed the modern theory of rationally connected varieties, establishing criteria for rational connectedness that connect to classical problems studied by Federigo Enriques and Francesco Severi, and provided applications to families of varieties over function fields related to work by Serge Lang and Yuri Manin.

His contributions to the study of singularities include deep results on log canonical and Kawamata log terminal singularities, building on foundations by Yujiro Kawamata and V. V. Shokurov, and his theorems on deformations and moduli of varieties influenced research on the moduli space structure akin to work by David Mumford and Mikhail Gromov. Kollár's book-length treatments synthesized techniques from complex analytic geometry and algebraic topology while interacting with ideas from Donaldson theory and Seiberg–Witten theory in neighboring fields. His probabilistic and arithmetic applications connected rational points on varieties with conjectures influenced by Gerd Faltings and Jean-Pierre Serre.

Kollár also made influential contributions to stable maps and stable reduction problems, relating to the work of Joe Harris, Ian Morrison, and contributors to the Deligne–Mumford compactification, and to classification problems that reflect the legacy of Alexander Grothendieck and David Mumford.

Awards and honors

Kollár's recognition includes the Cole Prize in algebra by the American Mathematical Society, the Shaw Prize in Mathematical Sciences, election to the National Academy of Sciences (United States), and membership in the Hungarian Academy of Sciences. He has been an invited speaker at the International Congress of Mathematicians and received honors from organizations such as the American Mathematical Society and the European Mathematical Society. Additional distinctions include fellowships at the Institute for Advanced Study and prizes associated with contributions to birational geometry celebrated by communities connected to the Clay Mathematics Institute and national academies worldwide.

Selected publications

- Kollár, J.; Mori, S. "Birational Geometry of Algebraic Varieties." (Monograph synthesizing MMP techniques related to Shigefumi Mori and Miles Reid). - Kollár, J. "Rational Curves on Algebraic Varieties." (Comprehensive treatment linked to questions posed by Federigo Enriques and Francesco Severi). - Kollár, J. "Singularities of the Minimal Model Program." (Expositions on log canonical and Kawamata log terminal singularities with connections to Yujiro Kawamata and V. V. Shokurov). - Kollár, J.; Shepherd-Barron, N.; Alexeev, V. "Stable Surfaces and Moduli." (Work related to Deligne–Mumford compactification and David Mumford). - Kollár, J.; Miyaoka, Y.; Mori, S. "Rationally Connected Varieties." (Foundational paper building on methods by Miyaoka and Mori).

Category:Hungarian mathematicians Category:Algebraic geometers