Robert V. Kohn

Robert V. Kohn

Robert Vita Kohn (born October 5, 1953 ) is an American mathematician.

Kohn studied at Harvard University (Bachelor's degree 1974), at the University of Warwick (Master's degree in 1975) and at Princeton University , where he received his doctorate in 1979 under Frederick Almgren . At the same time he was operations analyst Daniel H. Wagner Associates in 1976 and researcher at Exxon in 1979 . As a post-doc he was a Fellow of the National Science Foundation at the Courant Institute of Mathematical Sciences of New York University , of which he has been a permanent member since 1981 and where he has been a professor since 1988 and is now (2009) Deputy Director.

Kohn deals with mathematical problems in materials science such as movement of phase boundaries and movement driven by curvature, modeling of heterogeneous (composite) materials, their moduli of elasticity and their microstructures, elasticity-theoretical optimization from these composite structures, crystal growth, structure formation as a minimization problem of energy. For example, he investigated applications in photonics, polycrystalline plasticity, micro-magnets, martensite junction, materials with memory , electrical tomography. In this context, he investigated the non-convex variation problems that arise when investigating heterogeneous materials, in which an optimal mixture of the materials is sought. In general, these problems do not have a clear classical solution, since their local minima are unstable.

Kohn also deals with nonlinear partial differential equations. His 1982 work with Louis Nirenberg and Luis Caffarelli with partial results on the regularity of weak solutions of the Navier-Stokes equation is well known . He also examined the self-similarity of the solutions to nonlinear evolution equations.

In addition, he deals with financial mathematics (such as optimizing and hedging portfolios, option prices).

In 2006 he gave a plenary lecture at the ICM in Madrid ( Energy Driven Pattern Formation ). Since 2009 he has been a fellow of SIAM , whose Ralph E. Kleinman Prize he received in 1999. From 1984 to 1986 he was a Sloan Research Fellow . In 2007 he received the Keith Medal of the Royal Society of Edinburgh with Stefan Müller and others. In 1994/95 he was a Midwest Mechanics Lecturer. In 2014 he received the Leroy P. Steele Prize for his work with Nirenberg and Caffarelli in 1982 . In 2017 he was elected to the American Academy of Arts and Sciences . He is a fellow of the American Mathematical Society .

Fonts

• as editor with Andrej Cherkaev: Topics in the Mathematical Modeling of composite materials (= Progress in Nonlinear Differential Equations and their Applications. 31). Birkhäuser, Boston MA et al. 1997, ISBN 0-8176-3662-5 .
• as editor with Graeme W. Milton: Random Media and Composites. Proceedings of the SIAM Workshop on Random Media and Composites, Leesburg, Va, Dec. 7-10, 1988. SIAM, Philadelphia PA 1989, ISBN 0-89871-246-7 .
• as editor with Jerald L. Ericksen , David Kinderlehrer , Jacques-Louis Lions : Homogenization and effective moduli of materials and media (= The IMA Volumes in Mathematics and its Applications. 1). Springer New York, New York NY 1986, ISBN 1-4613-8648-9 .

Web links

• Homepage at the Courant Institute

Individual evidence

1. ↑ Robert V. Kohn in the Mathematics Genealogy Project (English)
2. ↑ Caffarelli, Kohn, Nirenberg Partial regularity of suitable weak solutions of the Navier-Stokes equations , Communications Pure and Applied Mathematics, Volume 35, 1982, pp. 771-831