Whitman was born in Detroit, MI, on February 28, 1926, into a very loving, Catholic family. But within a few years the Depression hit the motor city and everything collapsed -- jobs, mortgage, etc. -- and chaos reigned. And so the Fall of 1931 his Mother and Dad decided to head South in search of whatever jobs were out there. They found haven in Roanoke, VA, Spartenburg, SC, Tryon, NC, and finally in the Spring of 1933 they landed in New Orleans. This became their home. He went to public grade school, public high school, and finally with a scholarship he attended Tulane University -- during the War years from 1942 to 1945. He graduated with a degree in Civil Engineering and entered the work force. But he was soon stricken down with a debilitating disease and had to face almost certain death. But something happened and that dreadful sentence did not occur, and he was fortunate enough to enter the Jesuits in 1951. The humanities and philosophy studies were exciting and in 1957 he went off to Washington, D.C,, and started his Ph.D. degree in mathematics at The Catholic University of America under the renowned geometer, Dr. Katsumi Nomizu. He received the degree in 1961 and went on to theology studies, being ordained a priest in 1963. During these studies he had the great privilege of having the renowned Fr. John Courtney Murray, S.J., as the director of his Licentiate Degree in Theology.

He started his professional career teaching at Loyola University in New Orleans in 1967. After two years at Loyola University in New Orleans, he spent seven years (1967-1974) at the University of Houston, where he earned a tenured position of Associate Professor in the Department of Mathematics. It was during these years where the paper on finite deformation theory in elasticity was conceived. At the invitation of Professor Paul Schweitzer he joined (in 1974) the faculty of the Pontifícia Universidade Católíca of Rio de Janeiro, where he was a tenured Associate Professor. In 1982-83 he took a sabbatical year at the Vatican Observatory, where he joined the staff as an adjunct scientist in 1983. During this period he worked with Fr. William Stoeger of the Vatican Observatory staff on research on the project of Professor G.F.R. Ellis, and on harmonic maps using the space of all Lorentzian metrics in the theory of gravitation. This also initiated a long and fruitful collaboration with Professor Ronald Knill of Tulane University. He returned to the United States in 1989 and took the position of Lecturer at the College of the Holy Cross. In 1996 he joined the staff of the Vatican Observatory and was stationed at the Vatican Observatory Research Group at the University of Arizona as an research scientist. In 1998 he was appointed as a permanent member of the staff of the Vatican Observatory.

In 1963 along with Lawrence Conlon, presently at Washington University in St. Louis, he formed the Clavius Group of mathematicians. This is a group of lay and religious mathematicians who meet each summer at various mathematical centers and departments to form a Faith Community and to do mathematics at levels from research to study seminars on current topics of interest to the Group. As of this writing [Jan, 2000] we have met for 37 consecutive summers.

Research Interests

A listing of these interests all revolve around the area of Modern Differential Geometry, an interest engendered during graduate school by his thesis director, Dr. Katsumi Nomizu. The title of his thesis is Invariant Connections in Principal Fiber Bundles over Locally Homogeneous Spaces.

Because of the influence of the Vatican Observatory these interests frequently focused on the area of the Geometry of Pseudo-Riemannian manifolds and its applications to Theory of Relativity, Gravitation, and Cosmology.

However over the years from the first introduction of these objects by Dr. Nomizu he has had a special interest in Holonomy Groups and the Holonomy Problem.

The Holonomy Problem addresses the question of what are the possible "natural" geometries that one can place on a differentiable manifold. Of course one of these geometries is Lorentzian geometry, pertinent of the study of physical space of the astronomers. But all of the symmetric spaces -- which include the important spaces of constant curvature -- are also included. However there are certain exceptional cases which are under intense investigation at the present moment, and in particular ones with an indefinite metric, as Lorentzian geometry. These latter are less well understood and are the object of current research.

Publications:

L. Conlon, A. Whitman, "A note on holonomy." Proc. AMS, 16 (1965), 1046-1951

P. Schweitzer, A. Whitman, "Pontryagin polynomial residues of isolated foliation singularities." Foliations and Gelfand-Fuks Cohomology, Springer Verlag, 1978, 95-103

J. Pierce, A. Whitman, "Topological properties of the manifold of configurations for several simple elastic bodies." Archive for Rational Mechanics and Analysis, 74(1980), 101-113

A. Whitman, G. Schühly, "Quantificação das variáveis sócio-econômicas e psicossociais e sua interrelação". G. Schühly, Marginalidade, Agir Editora, 1981, 137-146

G. Ellis, S. Nel, R. Maartens, W. Stoeger, A. Whitman, "Ideal observational cosmology." Physics Reports, 124(1985), 316-417

W. Stoeger, A. Whitman, R. Knill, "The harmonic mapping character of Rosen's bimetric theory of gravity and the geometry of its harmonic mapping space." Journal of Mathematical Physics, 26(1985), 2032-2038

R. Knill, A. Whitman, W. Stoeger, "The decomposition and superposition of rank-one gravitational potential tensors." Contemporary Mathematics, 51(1986), 81-91

A. Whitman, R. Knill, W. Stoeger, "Some harmonic maps on pseudo-Riemannian manifolds." International Journal of Theoretical Physics, 25(1986), 1139-1153

R. Knill, W. Stoeger, and A. Whitman, "Axially Symmetric Solution to Rosen's Field Equations with Angular Momentum". International Journal of Theoretical Physics, 27(1988), 283-288.

R. Knill and A. Whitman, "The well-posedness of the Rosen's Field Equations". Contemporary Mathematics, 71(1988), 157-166

A. Whitman and W. Stoeger, "The Harmonic-Map Structure of the Axially Symmetric Stationary Einstein Equations". General Relativity and Gravitation, 24(1992), 641-658

A. Whitman. Mathematica and the First Year Calculus Program. Lecture Notes internally distributed at the College of the Holy Cross, 640 pp.