Introduction
Joan Sylvia Lyttle Birman (born May 30, 1927, in New York City) is an American mathematician, specializing in braid theory and knot theory. Her book Braids, Links, and Mapping Class Groups has become a standard introduction, with many of today's researchers having learned the subject through it. Birman is currently Research Professor Emerita at Barnard College, Columbia University, where she has been since 1973.
Education
Birman received her B.A. (1948) in mathematics from Barnard College and an M.A. (1950) in physics from Columbia University.
She received her Ph.D. in mathematics in 1968 from the Courant Institute (NYU) under the supervision of Wilhelm Magnus, when she was 41 years old. Her dissertation was titled Braid groups and their relationship to mapping class groups.
Career
Birman's first position was at the Stevens Institute of Technology (1968–1973). She also was a visiting professor at Princeton University during part of this period. In 1973, she joined the faculty at Barnard College. In 1987 she was selected by the Association for Women in Mathematics to be a Noether Lecturer; this lecture honors women who have made fundamental and sustained contributions to the mathematical sciences. She was a visiting scholar at the Institute for Advanced Study in the summer of 1988. She has also been a Sloan Foundation Fellow (1974–76) and a Guggenheim Foundation Fellow (1994–95). In 1996 she won the Chauvenet Prize.
In 2012 she became a fellow of the American Mathematical Society. Her doctoral students include Józef Przytycki.
Selected publications
- "Automorphisms of the fundamental group of a closed, orientable 2-manifold". Proc. Amer. Math. Soc. 21: 351–354. 1969. doi:10.1090/s0002-9939-1969-0239593-9. MR 0239593.
- "Abelian quotients of the mapping class of a 2-manifold". Bull. Amer. Math. Soc. 76: 147–150. 1970. doi:10.1090/s0002-9904-1970-12406-5. MR 0249603.
- Braids, links and mapping class groups. Annals of Mathematical Studies. Princeton U. Press. 1975. ISBN 0691081492.
- with Taizo Kanenobu: "Jones' braid-plat formula and a new surgery triple". Proc. Amer. Math. Soc. 102: 687–695. 1988. doi:10.1090/s0002-9939-1988-0929004-1. MR 929004.
- with Hans Wenzl: "Braids, link polynomials and a new algebra". Trans. Amer. Math. Soc. 313: 249–273. 1989. doi:10.1090/s0002-9947-1989-0992598-x. MR 992598.
- "Recent developments in braid and link theory". Mathematical Intelligencer. 13 (1): 52–60. 1991. doi:10.1007/bf03024073.
- Magnus, W. (1976). "Review: Braids, links and mapping class groups by Joan S. Birman" (PDF). Bull. Amer. Math. Soc. 82: 42–45. doi:10.1090/s0002-9904-1976-13937-7.