Joseph L. Taylor. Professor, 1971. B.S. 1963, Louisiana State University. Ph.D.,
1964, Louisiana State University. Chairman, Dept. of Mathematics, University of ...
Group Representations
Joseph L. Taylor
Professor, 1971 B.S. 1963, Louisiana State University Ph.D., 1964, Louisiana State University Chairman, Dept. of Mathematics, University of Utah, 1979--82 Dean, College of Science, University of Utah, 1985--87 Vice President, Academic Affairs, University of Utah, 1987--90 Phone: (801) 581-3927;
[email protected]
Activities and Awards
Sloan Fellow 1967-71 Distinguished Research Award, University of Utah, 1974 Invited Speaker, International Congress of Mathematicians, 1974 Steele Prize, American Mathematical Society,1975
Mathematical Interests Professor Taylor spent a year as a Benjamin Pierce instructor at Harvard immediately after receiving his Ph. D from Louisiana State University. He then joined the faculty of the University of Utah in 1965 where he has worked ever since, except during sabbaticals at Stanford and in England and Australia. Professor Taylor's early research interests were in the general area of Banach Algebra Theory. He worked on problems concerning operator algebras, algebras of measures under convolution and general commutative Banach algebras. More recently Professor Taylor's research interest have shifted into non-commutative harmonic analysis - specifically, the study of representations of semi-simple Lie groups.
Professor Taylor's research contributions include a counter-example to a theorem of Tomita claiming the existence of a certain direct integral decomposition of a C*-algebra, a description of the maximal ideal space of any convolution measure algebra and a computation of its cohomology groups, the introduction of a new notion of joint spectrum for a commuting family of operators and the proof of a corresponding holomorphic functional calculus and the development and investigation of homology and cohomology theories for the category of topological modules over a topological algebra. Later, he introduced a notion of
K-theory for Banach algebras which is analogous to Grothendieck K-theory for rings. This led to the extensive use of K-theory as a tool in the study of C* algebras. He also developed general methods for relating the algebraic structure of a commutative Banach algebra to various homotopy invariants of the maximal ideal space of the algebra. This work later led Professor Taylor to introduce a new group, similar to but larger than the Brauer group, associated to an algebra and to prove that it is isomorphic to a certain Etale cohomology group of the algebra. Most recently, in joint work with Henryk Hecht and with Laura Smithies, Professor Taylor established and studied an equivalence of categories between a derived category of representations of a semi-simple Lie group and a derived category of sheaves on the associated flag variety.
Selected Publications 1. A joint spectrum for several commuting operators, J. of Funct. Anal. 6 (1970) 172--181. 2. Cohomology of the spectrum of a measure algebra, Acta. Math. 126 (1971) 195--225. 3. Homology and cohomology for topological algebras, Advances in Math. 9 (1972) 137--182. 4. Topological invariants of the maximal ideal space of a Banach algebra, Advances in Math. 19 (1976) 149-206. 5. The bigger Brauer group and Etale cohomology (with Iain Raeburn), J. Aust. Math. Soc. 119 (1985) 445-463. 6. Analytic localization of group representations (with Henryk Hecht), Advances in Math. 79 (1990) 139-212.
www.math.utah.edu/~taylor
