Geoffrey Ross Goodson
Professor of Mathematics
I joined the faculty at
During 1992 I was the Maryland State 40+ Squash champion. I am married with three children, a son who completed a Ph.D. in Computer Engineering at Carnegie Mellon University and now works in hard drive storage research, a daughter who completed a master's degree in Geology at Georgia State University in Atlanta and is now working for the Department of the Environment in Maryland, and another daughter who completed a master's degree in Civil Engineering at Berkeley, and is now working for a Structural Engineering company in San Francisco.
My main research interests lie in
the ergodic and spectral properties of measure preserving transformations, but
I have recently been working on some problems in matrix and operator theory. I
am a member of the London Mathematical
Society and the American Mathematical
Society and the Mathematical Association of America. In the year 2000 I
· Spectral doubling of normal operators and connections with antiunitary operators. Integral Equations and Operator Theory, 72 (2011), 116-130.
· Groups having elements conjugate to their squares and connections with dynamical systems. Applied Mathematics, 1 (2010), 415-423.
· On commutators in matrix theory. Operators and Matrices, 4 (2010), 283-292.
· Canonical forms for normal matrices that commute with their complex conjugate. Linear Algebra and Applications, 4 (2010), 283-292. (with Roger Horn)
· Spectral properties of ergodic dynamical systems conjugate to their composition squares. Colloquium Mathematicum, 107 (2007), 99-118.
· On the multiplicity function of real normal operators. Operators and Matrices, 2 (2008), 1-13.
· Quasi-real normal matrices and eigenvalue pairings. the Journal of Linear Algebra and its Applications, 369 (2003) 279-294. (With Roger Horn and Dennis Merino)
· Conjugations between T and T^2 for ergodic transformations T. Acta Mathematica Universitatis Comenianae 71 (2002), 201-210.
· Laboratory Manuals for Single Variable and Multivariable Calculus. Coauthored with R. Boules, M. O'Leary and O. Kim and published by Harcourt, 2000.
· Conjugacies between ergodic transformations and their inverses. Colloquium Mathematicum 84 (2000), 185-193.
· Joining properties of ergodic dynamical systems having simple spectrum. Sankhya: Indian Journal of Statistics. 62 (2000), 376-386.
· A survey of recent results in the spectral theory of ergodic dynamical systems. Journal of Dynamical and Control Systems. 5 (1999), 173-226.
· Skew products in the centralizers of compact abelian group extensions. Acta Mathematica Universitatis Comenianae. 68 (1999), 171-178.
· The converse of the inverse-conjugacy theorem for unitary operators and ergodic dynamical systems. Proceedings of the American Mathematical Society. 128 (2000), 1381-1388.
Conjugations, joinings and direct
products of locally rank-one dynamical systems. Journal of
Dynamical and Control Systems. 3 (1997), 321-341. (with V. V. Ryzhikov).
(To load a dvi file, click here).
· Inverse conjugacies and reversing symmetry groups, The American Mathematical Monthly. 106 January (1999), 19-28
The structure of ergodic transformations
conjugate to their inverses. Ergodic Theory of Z^d-Actions.
Proceedings of the
(To see an abstract click here, to load dvi file, click here).
Transformations conjugate to their
inverses have even essential values. Proceedings of the AMS.
124 (1996), 2703-2710. (With M. Lemanczyk).
(To see an abstract click here, to load a dvi file, click here).
· Ergodic transformations conjugate to their inverses by involutions. Ergodic Theory and Dynamical Systems. 16 (1996), 97-124. (With M. Lemanczyk, A. del Junco and D. Rudolph).
Functional equations associated with the
spectral properties of compact group extensions. Ergodic Theory and
its Connections with Harmonic Analysis. Proceedings of the 1993