EqWorld

The World of Mathematical Equations

Francesco CALOGERO Professor

Born: 6 February 1935, Fiesole, Italy

Education:

• February 1958, graduated ["laurea in fisica"] cum laude in Rome

Current Professional Status:

• Professor of Theoretical Physics, University of Rome "La Sapienza", since 1976

Membership:

• Member (1987-1990), Scientific Secretary (1990-1993), Chairman (1993-1996) of the Mathematical Physics Commission of the International Union of Pure and Applied Physics (IUPAP);
• Editorial board of journal Reviews in Mathematical Physics;
• Editorial board of journal Methods of Functional Analysis and Topology;
• Editorial board of Journal of Nonlinear Mathematical Physics;
• Editorial board of website EqWorld: The World of Mathematical Equations

Honours:

• 1989-1997, Secretary General, Pugwash Conferences on Science and World Affairs (Nobel Prize for Peace, 1995)

Areas of Expertise:

• integrable nonlinear evolution partial differential equations,
• solvable dynamical systems,
• scattering theory,
• quantum field theory, nuclear many-body problem,
• special functions,
• finite-dimensional representations of operators, numerical computation of the eigenvalues of differential operators

Author:

• scientific publications (in English): 3 books and over 300 papers;
• publications on science and society: several books and about 390 papers (half in English)

Main Scientific Publications (Books):

• F. Calogero, Variable phase approach to potential scattering, Academic Press, New York, 1967 (translated into Russian in 1972).
• F. Calogero and A. Degasperis, Spectral transform and solitons, North Holland, Amsterdam, 1982 (translated into Russian in 1985).
• F. Calogero, Classical many-body problems amenable to exact treatments (Lecture Notes in Physics Monograph m66), Springer, 2001.

Some Results on Integrable Systems:

• introduction and solution of the quantum one-dimensional many-body problem with inverse square two-body potentials;
• discovery via the Lax technique of the integrability of a class of classical many-body problems (first introduction of elliptic interactions in many-body integrable models; first introduction of functional equations in this field);
• introduction of a new technique to identify integrable one-dimensional many-body problems, with many examples (later extended to rotation-invariant two-body problems);
• introduction of a new general technique to identify and investigate integrable nonlinear PDEs;
• spectral interpretation of Bäcklund transformations;
• identification of several new integrable nonlinear PDEs (with A. Degasperis);
• elaboration of the multiscale reduction technique (in the form introduced by W. Eckhaus) and introduction of the notion of "universal" equations, which are therefore both integrable and widely applicable;
• introduction of a technique to discover integrable many-body problems in ordinary (three-dimensional) space, with several new examples characterized by rotation-invariant Newtonian equations of motion (with M. Bruschi);
• introduction of the notion of "nonlinear harmonic oscillator", with interesting examples (with V. Inozemtsev);
• investigation of "isochronous systems" (system that possess an open region having full dimensionality in their phase space where all solutions are completely periodic with a fixed period), with the observation that "such systems are not rare" (indeed, almost any dynamical system can be deformed so that the deformed system is isochronous);
• investigation of the behavior of certain isochronous systems outside of their phased-space region of isochronicity, and of a mechanism to explain (as travel over Riemann surfaces) the transition from ordered to disordered motions, including the onset of a new kind of deterministic chaos.

Mailing Address:
Department of Physics
University of Rome "La Sapienza"
p. Aldo Moro
I-00185 ROMA (Italy)

E-mails: francesco.calogero@roma1.infn.it, calogero@uniroma1.it
Home page: http://www.phys.uniroma1.it/DOCS/TEO/people/calogero.txt

Page last updated: 14 April 2005

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