Howard Garland Explained

Howard Garland (born 27 October 1937, in Detroit)^[1] is an American mathematician, who works on algebraic groups, Lie algebras (structure theory and representation theory), and infinite-dimensional algebras.^[2]

Garland received in 1958 his bachelor's degree from the University of Chicago, in 1959 his master's degree from Wayne State University, and in 1964 his Ph.D. from the University of California, Berkeley under S. S. Chern with thesis On the cohomology of lattices in Lie groups). As a postdoc he was in 1964–1965 an instructor at Yale University and in 1965–1966 a visiting scholar at the Institute for Advanced Study.^[3] At Yale University he became in 1966 an assistant professor, in 1969 an associate professor, and in 1973 a full professor. Garland was a visiting professor in 1969–1970 at Columbia University and in 1972–1973 at the State University of New York at Stony Brook.

In 1986 Garland, with his doctoral student Igor Frenkel and with Gregg Zuckerman, applied Feigin's theory of semi-infinite cohomology of graded Lie algebras to explain some aspects of the BRST quantization of string theory.^[4]

Selected publications

• with W. C. Hsiang: A square integrability criterion for the cohomology of arithmetic groups. Proc Natl Acad Sci U S A. 59. 2. 1968. 354–360. 224677. 10.1073/pnas.59.2.354. 16591605. Garland H, Hsiang WC . 1968PNAS...59..354G. free.
• with M. Goto: Lattices and the adjoint group of a Lie group. Trans. Amer. Math. Soc.. 124. 1966. 450–460. 1994386. 10.1090/s0002-9947-1966-0199311-1. free. Garland. Howard. Goto. Morikuni. 3.
• A rigidity theorem for discrete subgroups. Trans. Amer. Math. Soc.. 129. 1967. 1–25. 1994361. 10.1090/s0002-9947-1967-0214102-1. free. Garland. Howard. 1.
• with M. S. Raghunathan: Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups. Annals of Mathematics. 92. 1970. 279–326. 1970838. 10.2307/1970838. Garland. H.. Raghunathan. M. S.. 2.
• A finiteness theorem for K _{2} of a number field. Annals of Mathematics. 94. 1971. 534–548. 1970769. 10.2307/1970769. Garland. Howard. 3.
• P-adic curvature and the cohomology of discrete subgroups of p-adic groups. Annals of Mathematics. 97. 1973. 375–423. 10.2307/1970829. 1970829. Garland. Howard. 3.
• with M. S. Raghunathan: A Bruhat Decomposition for the Loop Space of a Compact Group: A New Approach to Results of Bott. Proc Natl Acad Sci U S A. 72. 12. 1975. 4716–4717. 388799. 10.1073/pnas.72.12.4716. 16592292. Garland H, Raghunathan MS . 1975PNAS...72.4716G. free.
• The arithmetic theory of loop algebras. J. Algebra. 53. 1978. 480–551. 10.1016/0021-8693(78)90294-6. Garland. Howard. 2. free.
• with I. B. Frenkel and G. J. Zuckerman: Semi-Infinite Cohomology and String Theory. Proc Natl Acad Sci U S A. 83. 22. 1986. 8442–8446. 386946. 10.1073/pnas.83.22.8442. 16578792. Frenkel IB, Garland H, Zuckerman GJ . 1986PNAS...83.8442F. free.

References

1. biographical information from American Men and Women of Science, Thomson Gale 2004
2. http://users.math.yale.edu/public_html/People/hgarland.html Garland's homepage at Yale
3. http://www.ias.edu/people/cos/users/4517 Howard Garland | Institute for Advanced Study
4. Frenkel, I. B.. Garland, H.. Zuckerman, G. J.. Semi infinite cohomology and string theory. Proc Natl Acad Sci U S A. 83. 1986. 22. 8442–8446. 386946. 10.1073/pnas.83.22.8442. 16578792. 1986PNAS...83.8442F. free.