Joan Sylvia Lyttle Birman (born May 30, 1927) 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.
Birman received her B.A. (1948) in mathematics from Barnard College and an M.A. (1950) from Columbia University. She received her Ph.D. in 1968 from the Courant Institute (NYU) under the supervision of Wilhelm Magnus. Her dissertation was titled Braid groups and their relationship to mapping class groups.
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 to be a Noether Lecturer. 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.
- "Automorphisms of the fundamental group of a closed, orientable 2-manifold". Proc. Amer. Math. Soc. 21: 351–354. 1969. MR 0239593.
- "Abelian quotients of the mapping class of a 2-manifold". Bull. Amer. Math. Soc. 76: 147–150. 1970. 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. MR 929004.
- with Hans Wenzl: "Braids, link polynomials and a new algebra". Trans. Amer. Math. Soc. 313: 249–273. 1989. MR 992598.
- "Recent developments in braid and link theory". Mathematical Intelligencer 13 (1): 52–60. 1991.
- Joan Birman at the Mathematics Genealogy Project
- Institute for Advanced Study: A Community of Scholars
- Birman, Joan (1993). "New Points of View in Knot Theory". Bull. Amer. Math. Soc. (N.S.) 28: 253–287.
- List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- Magnus, W. (1976). "Review: Braids, links and mapping class groups by Joan S. Birman" (PDF). Bull. Amer. Math. Soc. 82: 42–45.
- Allyn Jackson and Lisa Traynor, Interview with Joan Birman, AMS Notices, January 2007, Volume 54, Number 1
- Homepage for Joan Birman
- "Joan Birman", Biographies of Women Mathematicians, Agnes Scott College
- O'Connor, John J.; Robertson, Edmund F., "Joan Birman", MacTutor History of Mathematics archive, University of St Andrews.
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