Yuri Manin

Yuri Manin
Gert-Martin Greuel · CC BY-SA 2.0 de · source
Name	Yuri Manin
Caption	Yuri Ivanovich Manin
Birth date	1937-02-16
Birth place	Kherson Oblast, Ukrainian SSR, Soviet Union
Death date	2023-03-01
Death place	Moscow, Russia
Nationality	Soviet / Russia
Fields	Mathematics
Alma mater	Moscow State University
Doctoral advisor	Igor Shafarevich
Known for	Algebraic geometry, Number theory, Mathematical physics, Quantum cohomology

Yuri Manin was a Soviet and Russian mathematician known for foundational work linking algebraic geometry, number theory, and mathematical physics. He made deep contributions to the theory of arithmetic geometry, moduli spaces, quantum groups, and mirror symmetry, influencing generations of mathematicians across Europe, North America, and Asia. His work connected classical problems studied by Bernhard Riemann, Alexander Grothendieck, and André Weil with modern developments involving Edward Witten, Maxim Kontsevich, and Michael Atiyah.

Early life and education

Manin was born in Kherson Oblast in the Soviet Union and grew up during the wartime and postwar period shaped by events such as World War II and the postwar rebuilding of Moscow. He studied at Moscow State University where he was exposed to the mathematical traditions of Andrey Kolmogorov, Israel Gelfand, and Sergei Novikov. His doctoral work was supervised by Igor Shafarevich, connecting him to the lineage of Alexander Grothendieck and André Weil through the Zeta function and Hasse principle problems studied at institutions like Steklov Institute and Institute for Advanced Study. During his student years he interacted with contemporaries including Yakov Sinai, Vladimir Arnold, and Lev Pontryagin.

Academic career and positions

He held positions at Moscow State University, the Steklov Institute of Mathematics, and spent visiting appointments at Institute for Advanced Study, Harvard University, Princeton University, University of Paris, ETH Zurich, and University of California, Berkeley. He lectured at universities such as Cambridge University, University of Oxford, Columbia University, University of Chicago, Massachusetts Institute of Technology, and research centers including CERN, Max Planck Institute for Mathematics, and Kavli Institute for Theoretical Physics. He collaborated with mathematicians at IHÉS, CNRS, and MPI Bonn, and participated in conferences like the International Congress of Mathematicians and seminars at Simons Center for Geometry and Physics.

Mathematical contributions

Manin's contributions span algebraic geometry, arithmetic geometry, number theory, mathematical physics, and algebra. He advanced the theory of moduli spaces building on ideas from Alexander Grothendieck and Igor Shafarevich, and introduced concepts connecting rational points to zeta functions influenced by Hasse and Weil. His work on the Manin obstruction (or Brauer–Manin obstruction) linked Brauer group methods with diophantine geometry studied by Jean-Pierre Serre and John Tate. He pioneered the use of theta functions and modular forms in counting rational points, extending themes from Srinivasa Ramanujan and Goro Shimura.

In algebraic topology and mathematical physics he contributed to quantum cohomology and mirror symmetry interacting with research of Maxim Kontsevich, Edward Witten, and Mikhail Gromov. He explored Frobenius manifolds and quantum groups linked to work by Vladimir Drinfeld, George Lusztig, and Nicholas Reshetikhin. His insights influenced developments in string theory, conformal field theory, and the mathematics of integrable systems studied by Lax, Zakharov, and Boris Dubrovin.

In algebra he made contributions to noncommutative geometry related to threads from Alain Connes and to the theory of theta divisors connecting to David Mumford and Arnaud Beauville. His blending of arithmetic and geometry drew on the legacy of Carl Friedrich Gauss, Bernhard Riemann, Emil Artin, and modernists like Pierre Deligne and Jean-Louis Verdier.

Awards and honors

He received numerous honors from organizations including the Lenin Prize, Wolf Prize in Mathematics, the Shaw Prize, and national recognitions such as Order of Lenin and State Prize of the Russian Federation. He was elected to academies including the Russian Academy of Sciences, the National Academy of Sciences (foreign member), the Royal Society (honorary associations), and held honorary degrees from University of Oxford, University of Paris, ETH Zurich, and Harvard University. He delivered plenary talks at the International Congress of Mathematicians and received medals from institutions such as Académie des Sciences and Max Planck Society.

Selected publications and students

His influential books and papers include monographs and articles published in venues associated with Springer-Verlag, Cambridge University Press, American Mathematical Society, and journals like Inventiones Mathematicae, Annals of Mathematics, Journal of the American Mathematical Society, and Compositio Mathematica. Notable works addressed cubic forms, zeta functions, quantum cohomology, and mirror symmetry. His students include prominent mathematicians who later held positions at Princeton University, Harvard University, University of Chicago, MIT, Stanford University, ETH Zurich, University of Cambridge, Imperial College London, Tel Aviv University, and Weizmann Institute; these students collaborated with scholars such as Pierre Deligne, Maxim Kontsevich, Aleksei Bondal, and Vladimir Drinfeld.

Personal life and legacy

Manin was part of a scholarly network involving figures like Andrey Kolmogorov, Israel Gelfand, Igor Shafarevich, and Sergei Novikov, influencing research cultures at Moscow State University and Steklov Institute. His legacy endures through concepts bearing his name used by researchers at IHÉS, Simons Foundation, Clay Mathematics Institute, and in programs at Europe's Mathematical Society and American Mathematical Society. Memorial conferences honoring him have been hosted by IHÉS, Institut Henri Poincaré, Mathematical Institute, Oxford, and Steklov Institute. He influenced interdisciplinary dialogues involving physicists at CERN and geometers at Max Planck Institute for Mathematics.

Category:Mathematicians