Manin (Yuri I. Manin)

Manin (Yuri I. Manin)
Name	Yuri I. Manin
Birth date	16 February 1937
Birth place	Moscow
Death date	1 March 2023
Death place	Zürich
Nationality	Soviet / Russian
Fields	Mathematics
Institutions	Moscow State University, Max Planck Institute for Mathematics, University of Bonn, Institut des Hautes Études Scientifiques, University of Chicago
Alma mater	Moscow State University
Doctoral advisor	Andrei Kolmogorov
Known for	Algebraic geometry, Number theory, Mathematical physics, Noncommutative geometry
Awards	Fields Medal?, Wolf Prize?, Lenin Prize?

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Manin (Yuri I. Manin) Yuri Ivanovich Manin was a prominent Soviet and Russian mathematician whose work spanned algebraic geometry, number theory, mathematical physics, and arithmetic geometry. He influenced generations through positions at Moscow State University, the Max Planck Institute for Mathematics, and guest appointments at institutions such as the Institute for Advanced Study and the University of California, Berkeley. His research connected themes from Alexander Grothendieck's program to developments in string theory and noncommutative geometry, earning widespread recognition across Europe and North America.

Early life and education

Manin was born in Moscow in 1937 into a family affected by the Soviet Union's intellectual milieu, receiving early schooling influenced by the legacy of mathematicians at Moscow State University, the Steklov Institute of Mathematics, and contemporaries of Andrei Kolmogorov, Israel Gelfand, Sergei Novikov, Luzin-era circles. He enrolled at Moscow State University where he studied under advisors linked to figures such as Kolmogorov, Pavel Alexandrov, Lev Pontryagin, Andrey Markov (family lineage), and completed doctoral work that connected to themes addressed by Emma Noether-inspired algebraists and the emerging Grothendieck school during the postwar period.

Manin contributed to the development of algebraic geometry through work on rational points, Diophantine geometry, and the study of cubic surfaces linked to classical problems from Joseph-Louis Lagrange's era, connecting to the Hasse principle, Brauer–Manin obstruction, and conjectures related to Manin's conjecture on distribution of rational points. He introduced influential ideas about moduli spaces and made contributions to Poincaré duality contexts, interacting with concepts from Alexander Grothendieck, Jean-Pierre Serre, John Tate, Goro Shimura, and Pierre Deligne. His work in mathematical physics explored links between quantum field theory, string theory, and mirror symmetry, intersecting with research by Edward Witten, Maxim Kontsevich, Alain Connes, and Michael Atiyah. Manin's writings advanced theta functions, Zeta functions, and structural aspects of Galois theory as developed by Évariste Galois-lineage scholars and modernizers such as Barry Mazur and Jean-Louis Colliot-Thélène.

Manin supervised and influenced a wide circle of students and collaborators connected to mathematical communities at Moscow State University, the Steklov Institute of Mathematics, IHÉS, MPI Bonn, and Princeton University. His collaborators included mathematicians from the generations of Sergei Gelfand, Boris Venkov-style algebraists, and later interactions with Maxim Kontsevich, Pierre Deligne, Alexander Beilinson, David Mumford, Gerd Faltings, Vladimir Drinfeld, Grigori Perelman-adjacent schools, and combinatorialists influenced by Paul Erdős. He engaged with interdisciplinary teams involving physicists such as Edward Witten, Nathan Seiberg, Cumrun Vafa, and geometers like William Fulton and Robin Hartshorne.

Manin received numerous recognitions and honors from mathematical bodies including fellowships and medals awarded by organizations like the Academy of Sciences of the USSR, the Russian Academy of Sciences, the European Mathematical Society, the International Mathematical Union, and prizes historically associated with Soviet and international honors such as the Lenin Prize, the Fields Medal-era peer recognition (though not a Fields recipient), and lifetime awards akin to the Wolf Prize. He delivered keynote addresses at the International Congress of Mathematicians and was elected to academies including the Academia Europaea, the National Academy of Sciences (foreign associate), and received honorary degrees from institutions like University of Chicago and ETH Zurich.

Manin's personal life intertwined with the vibrant intellectual milieus of Moscow and Western Europe; he maintained connections to institutions such as the Steklov Institute of Mathematics and international centers like IHÉS and the Max Planck Society. His legacy persists in textbooks, lecture notes, and collected papers that influenced curricula at Moscow State University, Harvard University, Princeton University, and research directions in arithmetic geometry, algebraic topology, and mathematical physics. Commemorations and symposia in his honor have taken place at universities including University of Bonn, ETH Zurich, Institute for Advanced Study, and research hubs like the Mathematical Sciences Research Institute, ensuring his ideas continue to shape ongoing work by contemporary mathematicians such as Peter Scholze, Bhargav Bhatt, Aise Johan de Jong, and Jacob Lurie.

Category:Mathematicians