Steven G. Krantz


Steven George Krantz is an American scholar, mathematician, and writer. Krantz is Professor Emeritus of Mathematics at Washington University in St. Louis. He has authored more than 350 research papers and published more than 150 books. Additionally, Krantz has edited journals such as the Notices of the American Mathematical Society and The Journal of Geometric Analysis.

Early life and education

Steven Krantz grew up in Redwood City, California and graduated from Sequoia High School in class of 1967.
Krantz was an undergraduate at the University of California, Santa Cruz. Krantz obtained his Ph.D. in mathematics from Princeton University in 1974 under the direction of Elias M. Stein and Joseph J. Kohn.

Biography

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.
He applied wavelet analysis to plastic surgery, creating software for facial recognition. Krantz has also written software for the pharmaceutical industry.
Krantz has worked on the inhomogeneous Cauchy–Riemann equations, on separate smoothness of functions, 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, The Implicit Function Theorem, Geometric Integration Theory, and The Geometry of Complex Domains. 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 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, 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.
In 2012 he became a Fellow of the American Mathematical Society. Krantz has an Erdős number of 1.
In the past year Krantz has collaborated with Arni S. R. Rao of Augusta University to study the COVID-19 epidemic. They have more than twenty
papers and book chapters as well as several virtual seminars on the topic.

Teaching

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 University of Science and Technology, the Mathematical Sciences Research Institute, the American Institute of Mathematics, Australian National University, Texas A&M, the University of Umeå, Uppsala University, the University of Oslo, Politecnico Torino, the University of Seoul, Université Paul Sabatier, and Beijing University.

Editor

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.

Awards and recognitions

  • Distinguished Teaching Award, UCLA Alumni Association, 1979
  • Chauvenet Prize of the MAA, 1992
  • Beckenbach Book Prize of the MAA, 1994
  • Outstanding Academic Book Award, Current Review for Academic Libraries, 1998
  • Sequoia High School Hall of Fame inductee, 2009
  • Listed in Who's Who and American Men and Women of Science
  • Fellow of the American Mathematical Society, 2012

    Selected publications

Krantz has published more than 350 scholarly articles and 160 books.
  • Freshman Calculus
  • Calculus: Single and Multivariable
  • Function Theory of Several Complex Variables
  • Function Theory of One Complex Variable
  • Complex Analysis: The Geometric Viewpoint
  • A Primer of Real Analytic Functions
  • The Implicit Function Theorem: History, Theory, and Applications
  • A Panorama of Harmonic Analysis
  • A Mathematician's Survival Guide
  • The Survival of a Mathematician
  • Mathematical Apocrypha
  • Mathematical Apocrypha Redux
  • Geometric Integration Theory
  • The Proof is in the Pudding: The Changing Nature of Mathematical Proof
  • The Geometry of Complex Domains
  • A Mathematician Comes of Age
  • Elements of Advanced Mathematics, 3rd ed.
  • Real Analysis and Foundations, 2nd ed.
  • A TeX Primer for Scientists
  • A Handbook of Typography for the Mathematical Sciences
  • Geometric Analysis of the Bergman Kernel and Metric
  • How to Teach Mathematics: Third Edition
  • The Theory and Practice of Conformal Geometry
  • I, Mathematician, I
  • I, Mathematician, II
  • A Primer of Mathematical Writing, 2nd edition
  • Harmonic and Complex Analysis in Several Variables
  • Geometric Analysis of the Bergman Kernel and Metric
  • A Guide to Functional Analysis
  • Foundations of Real Analysis
  • Convex Analysis
  • Essentials of Mathematical Thinking
  • Handbook of Complex Analysis
  • Transition to Analysis with Proof
  • Elementary Introduction to the Lebesgue Integral
  • ''An Episodic History of Mathematics: Mathematical Culture through Problem Solving''