:: Honors and
Awards
overview
............................................................................................................................................................................
Degrees: 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.
research summary
..........................................................................................................................................................
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.
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.
representative publications
..........................................................................................................................................................
:: "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. International
Conference 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
from 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)
.
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