Wolf graduated from at the University of Chicago with a bachelor's degree in 1956 and with his master's degree in 1957 and his Ph.D. under the supervision of Shiing-Shen Chern in 1959 (On the manifolds covered by a given compact, connected Riemannian homogeneous manifold).[1] From 1960 to 1962, as a post-doctoral researcher, he was at the Institute for Advanced Study in Princeton, New Jersey (and again from 1965 to 1966). In 1962 he was assistant professor and since 1966 he has been professor at Berkeley.
Wolf considered applications of group theory to differential geometry and complex manifolds and applications of harmonic analysis to the theory of elementary particles and control theory. In 1994 he received the Humboldt Research Award and in 1977 the Medal of the University of Liège. In 1989 he received an honorary professorship at the National University of Cordoba in Argentina. From 1972 to 1973 and from 1983 to 1984, he was a Miller Research Professor in Berkeley.
Joseph A. Wolf died on August 14, 2023, at the age of 86.[3]
Writings
Spaces of constant curvature, McGraw Hill 1967, 6. Edition AMS Chelsea Publ. 2011 ISBN978-0-8218-5282-8
Harmonic analysis on commutative spaces, American Mathematical Society, Mathematical Surveys and Monographs, Vol. 142, 2007[4]
Spherical functions on Euclidean space, J. Funct. Anal., volume 239, 2006, pp. 127–136 arXiv:math/0509459
With Gregor Fels, Alan HuckleberryCycle spaces of flag domains: a complex geometric viewpoint, Progress in Mathematics 245, Birkhäuser, 2006
Huckleberry, Alan T.; Wolf, Joseph A. (2002). "Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint". arXiv:math/0210445.
Classification and fourier inversion for parabolic subgroups with square integrable nilradical, Memoirs AMS 225, 1979
Unitary representations of maximal parabolic subgroups of the classical groups, Memoirs AMS 180, 1976
Representations on partially holomorphic cohomology spaces, Memoirs AMS 138, 1974
Editor Harmonic analysis and representations of semisimple Lie groups, (NATO Advanced Study Institute, Lüttich 1977), Reidel 1980
Principal series representations of direct limit groups, Compositio Mathematica, v. 141 (2005), pp. 1504–1530. arXiv:math/0402283
Complex forms of quaternionic symmetric spaces, in Complex, contact and symmetric manifolds, Progress in Mathematics 234, Birkhäuser 2005, pp. 265–277 arXiv:math/0308283
