2026 Joan S. Birman: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	42	1759	1527	754	610	117	10244

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

1759

1527

754

610

117

10244

Research.com Recognitions

2013 - Fellow of the American Mathematical Society
2012 - Fellow of the American Academy of Arts and Sciences
1994 - Fellow of John Simon Guggenheim Memorial Foundation
1974 - Fellow of Alfred P. Sloan Foundation

Overview

Joan S. Birman is affiliated with Columbia University in the United States and has contributed to the field of mathematics, particularly within the subfields of geometry and topology, mathematical physics, computer graphics and computer-aided design, applied mathematics, and theoretical computer science.

Their main research focuses cover a range of advanced mathematical topics, including:

Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Computational Geometry and Mesh Generation
Geometric Analysis and Curvature Flows
History and Theory of Mathematics

Birman has published extensively in several academic venues, with frequent publications in:

arXiv (Cornell University)
Notices of the American Mathematical Society
Involve a Journal of Mathematics
Geometriae Dedicata
Journal of Knot Theory and Its Ramifications

Some recent papers authored or coauthored by Birman include:

"Memories of Vaughan Jones" (2021), Notices of the American Mathematical Society
"On the Burau representation of B4" (2021), Involve a Journal of Mathematics
"Gassner and Burau representations over ℤ_p-modules" (2022), arXiv (Cornell University)
"Distance and intersection number in the curve graph of a surface" (2021), Geometriae Dedicata
"The work of Jones" (2022), arXiv (Cornell University)

Frequent collaborators in their work include Vasudha Bharathram, Dietmar Bisch, David Evans, Robion Kirby, and Sorin Popa.

Birman has been recognized by various scholarly organizations, receiving distinctions such as:

Fellow of the American Mathematical Society (2013)
Fellow of the American Academy of Arts and Sciences (2012)
Fellow of the John Simon Guggenheim Memorial Foundation (1994)
Fellow of the Alfred P. Sloan Foundation (1974)

Best Publications

Braids, Links, and Mapping Class Groups

Joan S. Birman

2415
Citations
Braids, link polynomials and a new algebra

Joan S. Birman;Hans Wenzl

675
Citations
Knot polynomials and Vassiliev's invariants

Joan S. Birman;Xiao-Song Lin

646
Citations
A new approach to the word and conjugacy problems in the braid groups

Joan Birman;Ki Hyoung Ko;Sang Jin Lee

538
Citations
New points of view in knot theory

Joan S. Birman

487
Citations
Braids, Links, and Mapping Class Groups. (AM-82)

Unknown

383
Citations
Mapping class groups and their relationship to braid groups

Joan S. Birman

353
Citations
Knotted periodic orbits in dynamical systems—I: Lorenz's equation

Unknown

343
Citations
Abelian and solvable subgroups of the mapping class groups

Joan S. Birman;Alex Lubotzky;John McCarthy

299
Citations
Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group

Joan S. Birman;Hugh M. Hilden

285
Citations
On braid groups

Joan S. Birman

269
Citations
Braids: A Survey

Joan S. Birman;Tara E. Brendle

235
Citations
Geodesics with bounded intersection number on surfaces are sparsely distributed

Joan S. Birman;Caroline Series

173
Citations
Studying links via closed braids. III. Classifying links which are closed 3-braids

Joan S. Birman;William W. Menasco

147
Citations
Heegaard splittings of branched coverings of

Joan S. Birman;Hugh M. Hilden

136
Citations
On Siegel's modular group

Joan S. Birman

132
Citations
On the homeotopy group of a non-orientable surface

Joan S. Birman;D. R. J. Chillingworth

122
Citations
Studying links via closed braids IV: composite links and split links

Joan S. Birman;William W. Menasco

117
Citations
Conjugacy in Garside groups I: cyclings, powers and rigidity

Joan S. Birman;Volker Gebhardt;Juan González-Meneses

107
Citations
The -invariant of 3-manifolds and certain structural properties of the group of homeomorphisms of a closed, oriented 2-manifold

Joan S. Birman;R. Craggs

104
Citations
On the Mapping Class Group of Closed Surfaces as Covering Spaces

Joan S. Birman;Hugh M. Hilden

77
Citations
A new approach to the word and conjugacy problems in the braid groups

Joan S. Birman;K.H. Ko;J.S. Lee

1
Citations

Frequent Co-Authors

Paolo Boldi University of Milan

Sebastiano Vigna University of Milan

Alexander Lubotzky Weizmann Institute of Science

External Links

Wikipedia of Joan S. Birman Personal website of Joan S. Birman

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