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Joan Birman

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Name  Joan Birman

Role  Mathematician
Joan Birman wwwawmmathorgnoetherbrochureGIFSBirmanjpg
Books  One-sided Heegaard Splittings and Homeotopy Groups of Some 3-manifolds
Education  Courant Institute of Mathematical Sciences (1968), Columbia University (1950), Barnard College (1948)
Awards  Chauvenet Prize, Noether Lecture, Guggenheim Fellowship for Natural Sciences, US & Canada

Interview with Joan Birman

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 learning the subject through it. Birman is currently Research Professor Emerita at Barnard College, Columbia University, where she has been since 1973.



Parents were George and Lillian Lyttle. Her father and mother were both immigrants. Her father was from Russia but grew up in Liverpool, England. While her mother was born in New York and her parents were Russian-Polish immigrants. At age 17, George emigrated to the US and became a successful dress manufacturer. Her father appreciated the opportunities from having a business but he wanted his daughters to focus on education.[1] She is married to Joseph Birman and has 3 kids.


After high school, Birman entered Swarthmore College, a coeducational institution in Swarthmore, Pennsylvania, and majored in mathematics. However, she disliked living in the dorms so she transferred to Barnard College, a women's only college affiliated to Colombia University, to live at home.

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. During her studies, she learned that she was more interested in pure mathematics than applied mathematics. 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 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. Then in 2005, she won the New York City Mayor's Award for Excellence in Science and Technology.

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. MR 0239593. doi:10.1090/s0002-9939-1969-0239593-9. 
  • "Abelian quotients of the mapping class of a 2-manifold". Bull. Amer. Math. Soc. 76: 147–150. 1970. MR 0249603. doi:10.1090/s0002-9904-1970-12406-5. 
  • 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. doi:10.1090/s0002-9939-1988-0929004-1. 
  • with Hans Wenzl: "Braids, link polynomials and a new algebra". Trans. Amer. Math. Soc. 313: 249–273. 1989. MR 992598. doi:10.1090/s0002-9947-1989-0992598-x. 
  • "Recent developments in braid and link theory". Mathematical Intelligencer. 13 (1): 52–60. 1991. doi:10.1007/bf03024073. 
  • References

    Joan Birman Wikipedia

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