Joan Birman

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Joan Sylvia Lyttle Birman
Born (1927-05-30) May 30, 1927 (age 92)
Alma materB.A., Barnard College, 1948
Ph.D., Courant Institute (NYU), 1968
Known forBraid theory, knot theory
AwardsChauvenet Prize
Scientific career
InstitutionsBarnard College, Columbia University
Doctoral advisorWilhelm Magnus
Doctoral students

Joan Sylvia Lyttle Birman (born May 30, 1927 in New York City[1]) is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is currently Research Professor Emerita at Barnard College, Columbia University, where she has been since 1973.


Her parents were George and Lillian Lyttle, both Jewish immigrants.[2] Her father was from Russia but grew up in Liverpool, England. 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. He appreciated the opportunities from having a business but he wanted his daughters to focus on education. She has three children. Her late husband, Joseph Birman, was a physicist and a leading advocate for human rights for scientists.[3]


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 Columbia University, to live at home.[2]

Birman received her B.A. (1948) in mathematics from Barnard College and an M.A. (1950) in physics from Columbia University. After working in the industry from 1950 to 1960, she did a PhD in mathematics at the Courant Institute (NYU) under the supervision of Wilhelm Magnus, graduating in 1968. Her dissertation was titled Braid groups and their relationship to mapping class groups.[4]


Birman's first position was at the Stevens Institute of Technology (1968–1973). In 1969 she published "On Braid Groups", which introduced the Birman Exact Sequence which became one of the most important tools in the study of braids and surfaces [5]. During the later part of this period she published a monograph, 'Braids, links, and mapping class groups' based on a graduate course she taught as a visiting professor at Princeton University in 1971-72. This book is considered the first comprehensive treatment of braid theory, introducing the modern theory to the field, and contains the first complete proof of Markov’s theorem [6].

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.[7] She was a visiting scholar at the Institute for Advanced Study in the summer of 1988.[8] She has also been a Sloan Foundation Fellow (1974–76) and a Guggenheim Foundation Fellow (1994–95). In 1996, she won the Chauvenet Prize.[9] Then in 2005, she won the New York City Mayor's Award for Excellence in Science and Technology.[1]

She supervised 21 doctoral students, and has a total of 50 academic descendants. Her doctoral students include Józef Przytycki.[4]

In 2017, she endowed the Joan and Joseph Birman Fellowship for Women Scholars at the American Mathematical Society to support mathematical research by mid-career women.[10]


Birman's scientific work includes 77 research publications and 16 expository articles or reviews. She is the author of the research monograph Braids, Links, and Mapping Class Groups.


In 2012, she became a fellow of the American Mathematical Society.[11] The Association for Women in Mathematics has included her in the 2020 class of AWM Fellows for "her groundbreaking research connecting diverse fields, and for her award-winning expository writing; for continuously supporting women in mathematics as an active mentor and a research role model; and for sponsoring multiple prize initiatives for women".[12]

Selected publications[edit]

  • Birman, Joan S.; Hilden, Hugh M. (1973). "On Isotopies of Homeomorphisms of Riemann Surfaces". Annals of Mathematics. 97 (3): 424–439. CiteSeerX doi:10.2307/1970830. JSTOR 1970830.
  • "Heegaard splittings of branched coverings of 𝑆³". Transactions of the AMS. 213: 315–352. 1975.
  • Birman, Joan S.; Lubotzky, Alex; McCarthy, John (1983). "Abelian and solvable subgroups of the mapping class groups". Duke Mathematical Journal. 50 (4): 1107–1120. doi:10.1215/S0012-7094-83-05046-9.
  • Birman, Joan S.; Williams, R.F. (1983). "Knotted periodic orbits in dynamical systems—I: Lorenz's equation". Topology. 22: 47–82. doi:10.1016/0040-9383(83)90045-9.
  • Birman, Joan S. (1985). "On the Jones polynomial of closed 3-braids". Inventiones Mathematicae. 81 (2): 287–294. doi:10.1007/BF01389053.
  • Birman, Joan S.; Wenzl, Hans (1989). "Braids, link polynomials and a new algebra". Transactions of the AMS. 313: 249–273. doi:10.1090/S0002-9947-1989-0992598-X.
  • Birman, Joan S.; Menasco, William W. (1990). "Studying links via closed braids IV: composite links and split links". Inventiones Mathematicae. 102: 115–139. arXiv:math/0407403. doi:10.1007/BF01233423.
  • Birman, Joan S.; Lin, Xiao-Song (1993). "Knot polynomials and Vassiliev's invariants". Inventiones Mathematicae. 111: 225–270. doi:10.1007/BF01231287.
  • Birman, Joan; Ko, Ki Hyoung; Lee, Sang Jin (1998). "A New Approach to the Word and Conjugacy Problems in the Braid Groups". Advances in Mathematics. 139 (2): 322–353. arXiv:math/9712211. doi:10.1006/aima.1998.1761.
  • Birman, Joan S.; Wrinkle, Nancy C. (2000). "On Transversally Simple Knots". Journal of Differential Geometry. 55 (2): 325–354. arXiv:math/9910170. doi:10.4310/jdg/1090340880.
  • Birman, Joan S.; Ko, Ki Hyoung; Lee, Sang Jin (2001). "The Infimum, Supremum, and Geodesic Length of a Braid Conjugacy Class". Advances in Mathematics. 164: 41–56. arXiv:math/0003125. doi:10.1006/aima.2001.2010.
  • Birman, Joan; Margalit, Dan; Menasco, William (2016). "Efficient geodesics and an effective algorithm for distance in the complex of curves". Mathematische Annalen. 366 (3–4): 1253–1279. arXiv:1408.4133. doi:10.1007/s00208-015-1357-y.
  • Braids, links and mapping class groups. Annals of Mathematical Studies. Princeton U. Press. 1975. ISBN 978-0691081496.[13]

See also[edit]


  1. ^ a b Larry Riddle. "Joan S. Birman", Biographies of Women Mathematicians, at Agnes Scott College
  2. ^ a b "Birman biography". Retrieved 2017-09-23.
  3. ^ "Joseph L. Birman (1927-2016)". Retrieved 2018-04-02.
  4. ^ a b Joan Sylvia Lyttle Birman at the Mathematics Genealogy Project
  5. ^ Margalit, Dan (2019). "The Mathematics of Joan Birman" (PDF). AMS Notices. 66 (3).
  6. ^ Margalit, Dan (2019). "The Mathematics of Joan Birman" (PDF). AMS Notices. 66 (3).
  7. ^ "Noether Lectures". Association for Women in Mathematics. Association for Women in Mathematics. Retrieved 2 September 2016.
  8. ^ Institute for Advanced Study: A Community of Scholars
  9. ^ Birman, Joan (1993). "New Points of View in Knot Theory". Bull. Amer. Math. Soc. (N.S.). 28 (2): 253–287. arXiv:math/9304209. doi:10.1090/s0273-0979-1993-00389-6.
  10. ^ "American Mathematical Society - The Joan and Joseph Birman Fellowship for Women Scholars". Retrieved 2018-04-02.
  11. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
  12. ^ 2020 Class of AWM Fellows, Association for Women in Mathematics, retrieved 2019-11-08
  13. ^ 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.

External links[edit]