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Meinhard E. Mayer

picture of Meinhard E. Mayer

Professor Emeritus, Physics & Astronomy
School of Physical Sciences

PH.D., Parhon University, Bucharest, 1957
M.S. EE, Polytechnic Institute, Bucharest, 1952

Phone: (949) 824-5543
Fax: (949) 824-2174

University of California, Irvine
2149 Frederick Reines Hall
Mail Code: 4575
Irvine, CA 92697
Research Interests
Mathematical Physics; Quantum Theory of Gauge Fields, Applications of Differential Geometry to Physics, Wavelet Transforms and Applications to Turbulence. Computational Physics: Symbolic and Numerical Computation in Scheme. Linux and applications.
Academic Distinctions
College de France Medal, 1985
Joint Institute for Nuclear Research, Dubna, USSR, 1957-1958
Research Abstract
Professor Mayer earned a MS in Electrical Engineering from the Polytechnic Institute Bucharest (1952), and a Ph.D. in Mathematical Physics (1957) from Parhon University, Bucharest (both in Romania). He was on the faculty of both these institutions. He held a postdoctoral position at the Joint Institute for Nuclear Research at Dubna, Russia, and was on the faculties of Brandeis University and Indiana University, before joining the UCI Physics and Mathematics Departments in 1966. He has held visiting positions at (among others) the University of Vienna (Austria), Imperial College (London), CERN, Geneva, College de France, Institute des Hautes Etudes Scientifiques, Ecole Normale Superieure (France) the Universities of Hamburg, Koln and Bonn (Germany), Hebrew University, Tel Aviv University, and the Weizmann Institute (Israel), University of Rome (Italy), and Harvard, MIT, Princeton University, Rutgers University, and NYU. During the last three decades, Professor Mayer's research interests have ranged from applications of differential geometry to gauge theories, to wavelet analysis of atmospheric turbulence, and symbolic computation applied to physics. Differential geometric methods are playing an ever-increasing role in mathematical physics, and in particular in particle theory and relativity. Professor Mayer was one of the pioneers in the use of the fiber-bundle description of gauge theories and has written one of the earliest texts on the subject. He has done research on the applications of groupoids in gauge theory. During the past few years, wavelet transform methods have become a very popular topic in applied mathematics and computation. A family of wavelets is generated from a "mother-wavelet" by scaling and translation and serves to decompose functions which exhibit self-similarity and scaling properties into spectra which can reveal interesting information about regions where significant changes in the "signal" occur. Professor Mayer has recently supervised two Ph.D. students who have applied wavelet transform methods respectively to pattern recognition in the Irvine-Michigan-Brookhaven proton decay experiment (E. Lulofs), and a wavelet cross-spectral analysis of turbulence (L. Hudgins). The latter method has been applied to an analysis of flows in the boundary layers between atmosphere and ocean and atmosphere and land, have revealed interesting large-scale coherent structures which are being investigated in a collaboration with Dr. L. Hudgins and Prof. Carl Friehe (ME). In the area of computational physics, Professor Mayer is collaborating with two colleagues at MIT in developing a mathematical library implemented in the Scheme dialect of Lisp, which is useful in symbolic and numerical computations using differential-geometric methods. In particular, they have published a book on how to do Lagrangian and Hamiltonian mechanics within this framework. Recent research interests are related to understanding the role of ghosts in "causal perturbation theory" and the relation of Loop Quantum Gravity to gauge theories. Professor Mayer has been teaching both undergraduate and graduate courses in Mathematical Physics, and has developed a computational physics course and lab, making use of the Scheme programming language. He has some expertise in Linux and Mac OS X system administration and software development. He has recently been teaching Freshman Seminars, mainly related to quantum and particle physics.
Outside of physics Professor Mayer has devoted some time to Yiddish and German poets and writers from Bukovina (where he grew up), and has offered a course on this subject at the Academy of Lifelong Learning.
Quantum Fields and Elementary Particles (in Romanian), Editura Tehnica, Bucharest, 1959
Introduction to the Fiber-Bundle Approach to Gauge Theories (138 pages) in Lecture notes in Physics, vol 67,
Springer Verlag New York, 1977
"Structure and Interpretation of Classical Mechanics" with Gerald J. Sussman and Jack Wisdom (MIT),534 pages. MIT Press,Cambridge, MA, 2001.
"Lie Groupoids versus Principal Bundles in Gauge Theories," in Proceedings of the International Conference on DifferentialGeometric Methods in Physics, L.-L. Chau and W. Nahm, Eds., Plenum Press, 1990.
"From Poisson Groupoids to Quantum Groupoids, and Back," in Proceedings of the XIX International Conference on DifferentialGeometric Methods in Physics, R. Cianci and U. Bruzzo, Eds. Rapallo, 1990; 12 pages, Springer Verlag, Heidelberg, 1991.
"Wavelet and Fourier Analysis of Atmospheric Turbulence", with L. Hudgins, C. Friehe, in Proc. Intern. Conf. on Wavelets, Toulouse, 1992, pp. 491-498; Y. Meyer and S. Roques, Eds., Frontieres, Gif, 1993.
The MIT Scheme Math Library "nscmutils" Reference Manual with Gerald J. Sussman, 1999
Professional Societies
Fellow, American Physical Society, since 1967
Lifetime Member, American Mathematical Society, International Association of Mathematical Physics
Other Experience
Visiting Professor
College de France 1985—1985

Visiting Professor
Institut des Hautes Etudes Scientifiques 1969—1970

Visiting Professor
University of Hamburg 1984—1985

Visiting Professor, Visiting Scholar
MIT, Cambridge, MA 1994—2001

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