Robert C. Hermann (April 28, 1931 – February 10, 2020) was an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between vector bundles on Riemannian manifolds and gauge theory in physics, before these interconnections became "common knowledge" among physicists in the 1970s.
Biography Born in Brooklyn, Hermann studied in Paris and at Princeton University, where he attended lectures by Charles Ehresmann and where in 1955 under Donald Spencer he received his PhD with thesis The Differential geometry of homogeneous spaces. He was a Benjamin Peirce Instructor at Harvard University in 1957, and researcher at MIT Lincoln Laboratory 1959 to 61 when he lectured at University of California Berkeley. In 1962 he became an associate professor at Northwestern University and was raised to full professor. In 1967 he taught at University of California Santa Cruz until moving to Rutgers University (1970 to 75). Subsequently he did research primarily with financial support from the Ames Research Center of NASA.Letters by Hermann published in Cartanian Geometry, Nonlinear Waves and Control Theory (1979) In the academic year 1969/1970 he was at the Institute for Advanced Study.
Following the French school of Élie Cartan, Hermann published numerous books on differential geometry and Lie group theory and their applications to differential equations, integrable systems, control theory, and physics. Most of these books were published in Brookline, Massachusetts by Math Sci Press, which he founded. Two series were published: a green series "Interdisciplinary Mathematics" and a blue series "Lie Groups: History, Frontiers and Applications".
The blue series considered history of differential geometry and Lie theory, and edited, with extensive new commentary, the work of Sophus Lie,Sophus Lie's 1884 differential invariant paper, 1976; Sophus Lie's 1880 transformation group paper, 1975 Gregorio Ricci-Curbastro and Tullio Levi-Civita,Ricci and Levi-Civita's tensor analysis paper, 1975 Felix Klein's Vorlesungen über Mathematikgeschichte,The Development of mathematics in the 19th Century, 1979 Élie Cartan,Geometry of Riemannian Spaces, 1983 Georges ValironThe geometric theory of ordinary differential equations, 1984; Classical differential geometry of curves and surfaces, 1986 and the contributions to invariant theory by David Hilbert.Hilbert's Invariant Theory Papers, 1978
Robert Hermann died on February 10, 2020.
Early works 1966: Lie Groups for Physicists, Benjamin 1968: Differential geometry and the calculus of variations, Academic Press, second edition, Brookline 1977 1969: Fourier analysis on groups and partial wave analysis, Benjamin 1970: Lie algebras and quantum mechanics, Benjamin 1970: Lectures in mathematical physics, Benjamin 1970: Vector Bundles in mathematical physics, Benjamin 1970 1973: Geometry, Physics and Systems, Dekker 1973: Differential geometric methods and ideas in physics and engineering, Rutgers University Press 1974: Physical Aspects of Lie group theory, Montreal, Presse Universitaire de Montreal
Published by Math Sci Press, Brookline, Massachusetts 1973, 1977: Topics in the mathematics of quantum mechanics 1973: Algebraic topics in systems theory 1973: General algebraic ideas 1973: Topics in General Relativity 1973: Energy-Momentum Tensors 1973: Linear and tensor algebra 1974: Spinors, Clifford and Cayley Algebras 1974: Linear systems and introductory algebraic geometry 1974: Geometric structure theory of systems-control theory and physics 1975: Gauge fields and Cartan–Ehresmann Connections 1977: The geometry of non-linear differential equations, Bäcklund transformations, and solitons 1977: (with Clyde Martin): Algebro-geometric and Lie theoretic techniques in systems theory 1977: Toda lattices, cosymplectic manifolds, Bäcklund transformations, and kinks 1977: Quantum and fermion differential geometry 1978: (with contributions by Frank Estabrook, Hugo Wahlquist) Yang–Mills, Kaluza–Klein, and the Einstein program 1979: Cartanian geometry, nonlinear waves, and control theory, Brookline, 2 parts: Part A, Part B 1980 (Cartanian meant in the sense of Élie Cartan) 1979: "Kleinian mathematics from an advanced standpoint", appendices to Felix Klein (M. Ackerman translator) Development of Mathematics in the 19th Century 1980: (with Norman Hurt) Quantum statistical mechanics and Lie group harmonic analysis 1984: Topics in the geometric theory of linear systems 1984: Topics in the geometric theory of integrable dynamical systems 1988: Topics in physical geometry 1991: Geometric computing science – first steps 1991: Geometric structures in nonlinear systems, Brookline 1991 (including hydrodynamics, deformation structures, with list of publications by Hermann to 1991) 1992: Constrained mechanics and Lie theory 1993: Lie–Cartan–Ehresmann Theory 1994: Lie-theoretic ordinary differential equations, numerical analysis, mechanics, and differential systems 1994: C–O–R generalized functions, current algebras and control
References
External links Books from Math-sci Press
Peter Cains & 7 others (2021) Memorial for Robert Hermann, Notices of the American Mathematical Society