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.
Professor Mayer has 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) 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 two 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 are preparing a text on how to do Lagrangian and Hamiltonian mechanics within this framework.
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.
"Lie Groupoids versus Principal Bundles in Gauge Theories," in Proceedings of the International Conference on Differential-Geometric 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 Differential-Geometric 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.
"Structure and Interpretation of Classical Physics," with Harold Abelson, Gerald J. Sussman and Jack Wisdom (MIT). Monograph-approx 500 pages January 2000.
The MIT Scheme Math Library "nscmutils" Reference Manual with Gerald J. Sussman, with contributions form Harold Abelson, Matthew Halfant, and other members of the MIT Scheme Team. To be completed.
"Wavelet Transforms and Atmospheric Turbulence," with Carl A. Friehe and Lonnie H. Hudgins, Physical Review Letters, 71, 3279-3282 (November 15, 1993)
"New Results on Wavelet Spectra in Atmospheric Turbulence," with L. Hudgins, and C. Friehe, in Wavelets: Theory, Algorithms, and Applications. Charles K. Chui, Laura Montefusco, and Lugia Puccio (eds.) (To be published by Academic Press, 1994.)