Research

Research Priorities: Algebraic geometry, number theory, differential equations, mathematical physics and computer science

Yuri Manin was a Russian-German mathematician. He made his main research contributions to the areas of algebraic geometry, number theory, differential equations, mathematical physics and computer science. He gave a proof of the Mordell conjecture for function fields by developing the Gauss-Manin connection, which is named after him.

Together with Russian mathematician Vasilii Iskovskikh, Yuri Manin found the first counterexample to the Lüroth problem. Furthermore, together with the British mathematicians Michael Francis Atiyah and Nigel Hitchin as well as with the Ukrainian-American mathematician Vladimir Drinfeld, he classified self-dual Yang-Mills fields (instantons). He proposed the theory of modular symbols and discovered the Brauer-Manin obstruction in the theory of Diophantine equations. He played a central role in the dialogue between mathematicians and theoretical physicists and was the originator of the idea for the quantum computer.

Career

• 2011-2023 Professor Emeritus, Department of Mathematics, Northwestern University, Evanston, USA
• 2005-2023 Professor Emeritus, Max Planck Institute for Mathematics, Bonn, Germany
• 2002-2011 Board of Trustees Professor, Department of Mathematics, Northwestern University,
• Evanston, USA
• 1995-2005 Director, Max Planck Institute for Mathematics, Bonn, Germany
• 1993-2005 Research Associate, Max Planck Institute for Mathematics, Bonn, Germany
• 1992-1993 Professor, Department of Mathematics, Massachusetts Institute of Technology (MIT),
• Boston, USA
• 1965-1992 Professor, Professorial Chair of Algebra, Moscow University, Moscow, Russia
• 1963 Habilitation, Moscow University, Moscow, Russia
• 1960-1993 Principal Researcher, Steklov Mathematics Institute, Lomonosov Moscow State University, Moscow, Russia
• 1960 PhD, Steklov Mathematics Institute, Lomonosov Moscow State University, Moscow, Russia

Functions

• Memberships in various editorial and advisory boards, including: Mathematical Sbornik, Uspekhi Matematicheskikh Nauk, Inventiones Mathematicae, Duke Mathematical Journal, Functional Analysis and its Applications, Crelle’s Journal, Journal of Number Theory, Journal of Geometry and Physics, Advances of Mathematics, International Journal of Mathematics, American Journal of Mathematics, Algebra & Number Theory

Honours and Memberships

• 2011 Honorary Member, London Mathematical Society, London, UK
• 2010 János Bolyai International Mathematical Prize, Hungarian Academy of Sciences, Hungary
• 2008 Great Cross of Merit with Star, Federal Republic of Germany
• 2007 Order Pour le Mérite for Sciences and Arts, Federal Republic of Germany
• from 2005 Foreign Member, Académie des Sciences, Paris, France
• from 2004 Fellow, American Academy of Arts and Sciences, Cambridge, USA
• 2002 Cantor Medal, German Mathematical Society, Germany
• 2002 King Faisal International Prize in Science, King Faisal Foundation, Saudi Arabia
• from 2000 Member, German National Academy of Sciences Leopoldina, Germany
• 1999 Honorary Professor, Sorbonne University, Paris, France
• 1999 Rolf Schock Prize for Mathematics, Royal Swedish Academy of Sciences, Sweden
• from 1996 Corresponding Member, Göttingen Academy of Sciences and Humanities, Göttingen, Germany
• from 1996 Member, Pontifical Academy of Sciences, Vatican City, Italy
• 1994 Frederic Esser Nemmers Prize for Mathematics, Northwestern University, Evanston, USA
• from 1993 Member, Academia Europaea
• from 1990 Foreign Member, Russian Academy of Sciences, Russia
• from 1990 Member, Royal Netherlands Academy of Arts and Sciences, Amsterdam, The Netherlands
• 1987 Brouwer Gold Medal, Royal Dutch Mathematical Society, The Netherlands
• 1967 Lenin Prize, Soviet Union
• 1963 Moscow Mathematical Society Prize, Moscow, Soviet Union