Research

Research Priorities: Algebraic geometry, topology, algebra, theory of algebraic cobordism, motivic cohomology, algebraic K-theory

Marc N. Levine is an American mathematician whose research centres on algebraic geometry. He analyses the structures of mathematical equations and develops mathematical methods. He and the French mathematician Fabien Morel jointly developed the theory of algebraic cobordism, which combines geometry, topology, and algebra.

Algebraic geometry deals with geometric spaces that are defined by equations. In mathematics, topology is concerned with spatial objects and how they relate to each other in space. Marc N. Levine uses methods from topology to help solve mathematical equations and questions from the field of algebra. He investigates the structural characteristics of equations. Applying this method to a mathematical equation results in the formation of a spatial object consisting of geometric forms, such as circles, ellipses, cubes, and spheres.

He and Fabien Morel jointly developed the theory of algebraic cobordism. Cobordism defines an equivalence relation that allows a set to be divided into subsets. The theory combines geometry, topology, and algebra. Geometric-topological descriptions can thus be applied to algebra, while concepts such as cobordism could also be transferred from topology to algebra. The theory of algebraic cobordism allowed Marc N. Levine and Fabien Morel to derive various mathematical propositions.

Other key research areas of interest to Marc N. Levine are motivic cohomology, motivic homotopy, and algebraic K-theory. K-theory is used in both quantum physics and string theory.

Career

• since 2009 Humboldt Professorship, University of Duisburg-Essen, Duisburg/Essen, Germany
• 2006-2007 Humboldt Senior Research Fellow, University of Duisburg-Essen, Duisburg/Essen, Germany
• 2005 Guest Fellow, University Paris VI, Paris, France
• 2004 Guest Fellow, Institut Henri Poincaré, Paris, France
• 2002-2003 Wolfgang Paul Programme, University of Duisburg-Essen, Duisburg/Essen, Germany
• 1998-1999 Visiting Professor, University of Essen, Essen, Germany
• 1995-1996 Visiting Professor, University of Essen, Essen, Germany
• since 1988 Professor, Northeastern University, Boston, USA
• 1986-1988 Associate Professor, Northeastern University, Boston, USA
• 1984-1986 Assistant Professor, Northeastern University, Boston, USA
• 1979-1984 Assistant Professor, University of Pennsylvania, Philadelphia, USA
• 1983 Guest Fellow, Max Planck Institute for Mathematics, Bonn, Germany
• 1974-1979 Lecturer, Brandeis University, Waltham, USA
• 1979 Doctorate, Brandeis University, Waltham, USA
• 1974 B.Sc., Massachusetts Institute of Technology (MIT), Boston, USA

Projects

• 2015-2024 Spokesperson, Priority Programme (PP) 1786 “Homotopy Theory and Algebraic Geometry”, German Research Foundation (DFG), Germany
• 2018-2022 Subproject “Enumerative geometry with quadratic forms”, PP 1786, DFG, Germany
• 2015-2022 Subproject “Applying motivic filtrations”, PP 1786, DFG, Germany
• 2015-2020 Subproject “Motives with modulus”, PP 1786, DFG, Germany
• 2015-2018 Subproject “Mixed Hodge structures in homotopy theory”, PP 1786, DFG, Germany
• 2011-2019 Subproject “Periods and Motives”, Transregio (TRR) 45, DFG, Germany
• 2011-2019 Subproject “Rational Points”, TRR 45, DFG, Germany
• 2008-2011 “Motivic homotopy theory”, National Science Foundation (NSF), USA
• 2005-2008 “Algebraic homotopy theory and algebraic cycles”, NSF, USA
• 2002-2005 “Cohomology theories for algebraic varieties”, NSF, USA
• 1994-2002 “K-theory and motivic cohomology”, NSF, USA
• 1991-1994 “Research in K-theory”, NSF, USA
• 1989-1991 “K-theory of fields”, NSF, USA
• 1987-1989 “K-theory”, NSF, USA
• 1985-1987 “Research in algebraic geometry”, NSF, USA
• 1983-1985 “Classification and deformations of complex manifolds”, NSF, USA
• 1981-1982 “Modern geometric methods in algebra”, NSF, USA

Honours and Memberships

• since 2018 Member, Academia Europaea
• 2018 Senior Berwick Prize, London Mathematical Society, London, UK
• since 2013 Member, German National Academy of Sciences Leopoldina, Germany
• 2006 Humboldt Research Award, Alexander von Humboldt Foundation, Bonn, Germany
• 2001 Wolfgang Paul Award, Alexander von Humboldt Foundation, Bonn, Germany