Robert Hermann

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Robert Hermann (born April 28, 1931 in Brooklyn ; † February 10, 2020 ) was an American mathematician and mathematical physicist .

Hermann studied in Paris and at Princeton University (where he heard lectures from Charles Ehresmann , among others ), where he obtained his doctorate under Donald Spencer in 1955 ( The Differential geometry of homogeneous spaces ). He taught at Rutgers University , left it around 1975 and then researched mainly with funds from the Ames Research Center at NASA . In 1969/70 he was at the Institute for Advanced Study .

Hermann published numerous books on differential geometry (especially based on the French school of Élie Cartan ) and Lie group theory and their applications to differential equations, integrable systems, control theory and physics, mostly published by the Mathematical Science Press in Brookline, Massachusetts, which he founded. He also emphasized the historical component and also re -edited works by Sophus Lie , Gregorio Ricci-Curbastro and Tullio Levi-Civita , Felix Klein's lectures on the history of mathematics, Élie Cartan, Georges Valiron and invariant theoretical works by David Hilbert with commentary.

In the 1960s he dealt with elementary particle physics and quantum field theory. As early as the 1960s he published books in which he pointed out the connection between the theory of fiber bundles based on Riemannian manifolds and physics ( gauge theories ), which only became "common property" among physicists from the 1970s onwards.

He was married to Lana Hermann and had a son and a daughter.

Books

  • Lie groups for physicists , Benjamin 1966
  • Fourier analysis on groups and partial wave analysis , Benjamin 1969
  • Lie algebras and quantum mechanics , Benjamin 1970
  • Lectures in mathematical physics , Benjamin 1970
  • Vector Bundles in mathematical physics , Benjamin 1970
  • Geometry, Physics and Systems , Dekker 1973
  • Differential geometry and the calculus of variations , Academic Press 1968, 2nd edition Brookline 1977
  • Differential geometric methods and ideas in physics and engineering , Rutgers University Press, 1973
  • Physical Aspects of Lie group theory , Montreal, Presse Universitaire de Montreal, 1974

In the Mathematical Science Press, Brookline, Massachusetts:

  • Topics in the mathematics of quantum mechanics , Brookline, 1973, 1977
  • with Clyde Martin: Algebro-geometric and Lie theoretic techniques in control theory , Brookline 1977
  • Algebraic topics in systems theory , Brookline 1973
  • General algebraic ideas , Brookline 1973
  • Topics in General Relativity , Brookline 1973
  • Energy-Momentum Tensors , Brookline 1973
  • Cartanian geometry, nonlinear waves and control theory , Brookline, 2 parts 1980 (Cartanian means in the sense of Elie Cartan)
  • Geometric structure theory of systems-control theory and physics , Brookline 1974
  • Constrained mechanics and Lie theory , Brookline 1992
  • Topics in the geometric theory of linear systems , Brookline 1984
  • Yang-Mills, Kaluza-Klein and the Einstein program , Brookline 1978 (with contributions by Frank Estabrook, Hugo Wahlquist)
  • Topics in the geometric theory of integrable dynamical systems , Brookline 1984
  • Linear and tensor algebra , Brookline 1973
  • Gauge fields and Cartan-Ehresmann Connections , Brookline 1975
  • Topics in physical geometry , Brookline 1988
  • with Norman Hurt: Quantum statistical mechanics and Lie group harmonic analysis , Brookline 1980
  • Toda lattices, cosymplectic manifolds, Bäcklund transformations, and kinks , Brookline 1977
  • The geometry of non-linear differential equations, Bäcklund transformations, and solitons , Brookline 1977
  • Geometric structures in nonlinear systems , Brookline 1991 (including hydrodynamics, deformation structures, with a list of publications by Hermann until 1991)
  • Spinors, Clifford and Cayley Algebras , Brookline 1974
  • Linear systems and introductory algebraic geometry , Brookline 1974
  • Lie-Cartan-Ehresmann Theory , Brookline 1993
  • Lie-theoretic ordinary differential equations, numerical analysis, mechanics, and differential systems , Brooklyn 1994
  • COR generalized functions, current algebras and control , Brookline 1994
  • Geometric computing science - first steps , Brookline 1991
  • Quantum and fermion differential geometry , Brookline 1977

Web links

Individual evidence

  1. ↑ DR. ROBERT C. HERMANN . Accessed February 16, 2020.
  2. ^ Letters from Hermann reprinted in "Cartanian geometry, nonlinear waves and control theory" 1979
  3. ↑ Sophus Lies 1884 differential invariant paper , 1976; Sophus Lies 1880 transformation group paper , 1975
  4. ↑ Ricci and Levi-Civitas tensor analysis paper , 1975
  5. ^ The Development of mathematics in the 19th Century , 1979
  6. ^ Geometry of Riemannian Spaces , 1983
  7. ^ The geometric theory of ordinary differential equations , 1984; Classical differential geometry of curves and surfaces , 1986
  8. ^ Hilbert's Invariant Theory Papers , 1978
personal data
SURNAME Hermann, Robert
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 28, 1931
PLACE OF BIRTH Brooklyn , New York City , New York , United States
DATE OF DEATH February 10, 2020