Research

Research Priorities: Algebraic geometry, number theory, algebraic varieties, rational Points

Yuri Tschinkel is a German-Russian mathematician. He works in the field of arithmetic geometry. He especially studies the rationality of varieties and the existence and distribution of rational points.

Yuri Tschinkel’s research moves at the interface between algebraic geometry and number theory. Algebraic geometry connects abstract algebra with geometry. It is concerned with geometric entities that can be described with equations, such as circles, ellipses, or cones. Number theory inquires into the qualities of integral and rational numbers, especially into solutions for equations with more than one variable.

Yuri Tschinkel studies algebraic varieties, their hidden symmetries, and rational points. Algebraic varieties are geometrical objects that are defined by polynomial equations. The points of these varieties are also used to describe geometrical facts. Methods of algebraic theory are part of numerous fields within mathematics and are also important to physics.

Yuri Tschinkel was the executive producer of the documentary “Colors of Math“.

Career

• since 2005 Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York City, USA
• 2003-2008 Professor, Gauß-Chair, Georg-August-Universität Göttingen, Göttingen, Germany
• 1999-2003 Associate Professor, University of Illinois at Chicago (UIC), Chicago, USA
• 1995-1996 Leibniz Fellow, École Normale Supérieure, Paris, France
• 1992-1995 Junior Fellow, Harvard Society of Fellows, Harvard University, Cambridge, USA
• 1992 PhD in Mathematics, Massachusetts Institute of Technology (MIT), Boston, USA
• 1985-1990 Studies in Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia
• Guest Researcher, Institut des hautes études scientifiques (IHES), Bures-sur-Yvette, France
• Guest Researcher, Max-Planck-Institute for Mathematics, Bonn, Germany
• Guest Researcher, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
• Guest Researcher, Princeton University, Princeton, USA
• Guest Researcher, Research Institute for Mathematical Sciences (RIMS), Kyoto and Tokyo, Japan

Functions

• since 2014 Trustee, Simons Center for Geometry and Physics (SCGP), Stony Brook University, Stony Brook, USA
• since 2012 Member, Scientific Advisory Board, ArXiv, Cornell University, Ithaca, USA
• since 2012 Member, Curatorium, Simons Institute for the Theory of Computing, University of California (UC) Berkeley, Berkeley, USA
• since 2012 Head, Division “Mathematics and Physical Sciences (MPS)”, Simons Foundation, New York City, USA
• since 2008 Scientific Advisory Board, Department of Mathematics and Applications (DMA), Ecole Normale Superieure, Paris, France
• 2013-2016 Scientific Advisory Board, Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University, Providence, USA
• 2010-2015 Scientific Advisory Board, Foundation Sciences Mathematiques de Paris, Paris, France
• 2008-2012 Advisory Board, Friends of IHES, Bures-sur-Yvette, France
• Member, Editorial Board, Algebraic Geometry, Experimental Mathematics
• Member, Editorial Board, Bulletin of the American Mathematical Society
• Member, Editorial Board, European Journal of Mathematics
• Member, Editorial Board, Research in Mathematical Sciences
• Member, Editorial Board, Journal of Algebraic Combinatorics
• Member, Editorial Board, Progress in Mathematics series

Projects

• 2016 Principal Investigator, Standard Grant “Birational Geometry and Rational Points”, National Science Foundation (NSF)
• 2010-2014 Member, Focused Research Group (FRG), Collaborative Research “Arithmetic and geometry of rational curves on K3 surfaces”, NSF, USA
• 2008-2012 Member, Research Training Group in Number theory, NSF, USA
• 2006-2010 Member, FRG, Collaborative Research “Geometry of moduli spaces of rational curves with applications to Diophantine problems over function fields”, NSF, USA
• 1999-2008 Participating Researcher, Research Training Group (GRK) 535 “Groups and Group Theory”, German Research Foundation (DFG), Germany

Honours and Memberships

• since 2021 Member, Academia Europaea
• since 2018 Member, German National Academy of Sciences Leopoldina, Germany
• since 2014 Fellow, American Association for the Advancement of Science (AAAS), USA
• since 2012 Fellow, American Mathematical Society, USA