**Geoffrey Ross Goodson
Professor of Mathematics**

Telephone: 410-704-2893

I joined the faculty at __University
of the Witwatersrand __in __University of Cape Town.__
Although I was born in the Cape Province of South Africa, I was brought up and
educated in __University
of Hull, U.K.,__ my master's degree from the __University of Warwick, U.K.,__ and
my doctorate from the __University of
Sussex, U.K.__

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
won the

·
**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 inverse-similarity problem for real
orthogonal matrices.** *The American Mathematical Monthly.* 104 March
(1997), 223-230.

(To see an __abstract
click here,__ to load __a dvi file, click here).__

·
**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

Last updated on June, 2012.