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Steven George Krantz
Steven G. Krantz in 2009
|Alma mater||University of California at Santa Cruz, Princeton University|
|Known for||Complex analysis|
Partial differential equations
Geometric measure theory
Randi D. Ruden (m. 1974)
|Institutions||UCLA, Penn State, Washington University in St. Louis|
|Doctoral advisor||Elias M. Stein, Joseph J. Kohn|
Steven George Krantz (born February 3, 1951) is an American scholar, mathematician, and writer. He has authored more than 250 research papers and more than 135 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.
Krantz was an undergraduate at the University of California, Santa Cruz (UCSC), graduating with summa cum laude in 1971. In the math department at UCSC his teachers included Nick Burgoyne, Marvin Greenberg, Ed Landesman, and Stan Philipp. Krantz obtained his Ph.D. in mathematics from Princeton University in 1974 under the direction of Elias M. Stein and Joseph J. Kohn. Other influencers included Fred Almgren, Robert Gunning, and Ed Nelson.
Among Krantz's research interests include: several complex variables, harmonic analysis, partial differential equations, differential geometry, interpolation of operators, Lie theory, smoothness of functions, convexity theory, the corona problem, the inner functions problem, Fourier analysis, singular integrals, Lusin area integrals, Lipschitz spaces, finite difference operators, Hardy spaces, functions of bounded mean oscillation, geometric measure theory, sets of positive reach, the implicit function theorem, approximation theory, real analytic functions, analysis on the Heisenberg group, complex function theory, and real analysis.
Krantz has worked on the inhomogeneous Cauchy-Riemann equations (he obtained the first sharp estimates in a variety of nonisotropic norms), on separate smoothness of functions (most notably with hypotheses about smoothness along integral curves of vector fields), on analysis on the Heisenberg group and other nilpotent Lie groups, on harmonic analysis in several complex variables, on the function theory of several complex variables, on the harmonic analysis of several real variables, on partial differential equations, on complex geometry, on the automorphism groups of domains in complex space, and on the geometry of complex domains. He has worked with Siqi Fu, Robert E. Greene, Alexander Isaev and Kang-Tae Kim on the Bergman kernel, the Bergman metric, and automorphism groups of domains; with Song-Ying Li on the harmonic analysis of several complex variables; and with Marco Peloso on harmonic analysis, the inhomogeneous Cauchy-Riemann equations, Hodge theory, and the analysis of the worm domain. Krantz's book on the geometry of complex domains, written jointly with Robert E. Greene and Kang-Tae Kim, appeared in 2011.
Krantz's monographs include Function Theory of Several Complex Variables, Complex Analysis: The Geometric Viewpoint, A Primer of Real Analytic Functions (joint with Harold R. Parks), The Implicit Function Theorem (joint with Harold Parks), Geometric Integration Theory (joint with Harold Parks), and The Geometry of Complex Domains (joint with Kang-Tae Kim and Robert E. Greene). His book The Proof is in the Pudding: A Look at the Changing Nature of Mathematical Proof looks at the history and evolving nature of the proof concept. Krantz's latest book, A Mathematician Comes of Age, published by the Mathematical Association of America, is an exploration of the concept of mathematical maturity.
Krantz is author of textbooks and popular books. His books Mathematical Apocrypha and Mathematical Apocrypha Redux are collections of anecdotes about famous mathematicians. Krantz's book An Episodic History of Mathematics: Mathematical Culture through Problem Solving is a blend of history and problem solving. A Mathematician's Survival Guide and The Survival of a Mathematician are about how to get into the mathematics profession and how to survive in the mathematics profession. Krantz's new book with Harold R. Parks titled A Mathematical Odyssey: Journey from the Real to the Complex is an entree to mathematics for the layman. His book I, Mathematician (joint with Peter Casazza and Randi D. Ruden) is a study, with contributions from many mathematicians, of how mathematicians think of themselves and how others think of mathematicians. The book The Theory and Practice of Conformal Geometry is a study of classical conformal geometry in the complex plane, and is the first Dover book that is not a reprint of a classic but is instead a new book.
Krantz has had 9 Masters students and 20 Ph.D. students. Among the latter are Xiaojun Huang (holder of the Bergman Prize), Marco Peloso, Fausto Di Biase, Daowei Ma, and Siqi Fu.
Krantz has organized conferences, including the Summer Workshop in Several Complex Variables held in Santa Cruz in 1989 and attended by 250 people. He was the principal lecturer at a CBMS conference at George Mason University in 1992. He organized and spoke at a conference on the corona problem held at the Fields Institute in Toronto, Canada in June 2012.
Krantz has taught at University of California, Los Angeles, Princeton University, Pennsylvania State University, and Washington University in St. Louis, where he served as chair of the mathematics department. He has been a visiting faculty member at the Institute for Advanced Study, Princeton, the University of Paris, the Universidad Autónoma de Madrid, Pohang Institute of Science and Technology, the Mathematical Sciences Research Institute, the American Institute of Mathematics, Australian National University (as the Richardson Fellow), Texas A&M (as the Frontiers Lecturer), the University of Umeå, Uppsala University, the University of Oslo, Politecnico Torino, the University of Seoul, Université Paul Sabatier, and Beijing University.
Krantz was editor-in-chief of the Notices of the American Mathematical Society for 2010 through 2015. Krantz is also editor-in-chief of the Journal of Mathematical Analysis and Applications and managing editor and founder of the Journal of Geometric Analysis. He also edits for The American Mathematical Monthly, Complex Variables and Elliptic Equations, and The Bulletin of the American Mathematical Society. Krantz is editor-in-chief of the new Springer journal titled Complex Analysis and its Synergies.
Krantz has published more than 230 scholarly articles and 130 books.