Benson Farb | |
|---|---|
 Farb at Oberwolfach, 2016 | |
| Born | October 25, 1967 |
| Nationality | American |
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| Spouse | |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Chicago |
| Doctoral advisor | William Thurston |
| Doctoral students | |
Benson Stanley Farb (born October 25, 1967) is an American mathematician at the University of Chicago. His research fields include geometric group theory and low-dimensional topology.
A native of Norristown, Pennsylvania, Farb earned his bachelor's degree from Cornell University.[ citation needed ] In 1994, he obtained his doctorate from Princeton University, under supervision of William Thurston. [1]
Farb has advised over 40 students, including Pallavi Dani, Kathryn Mann, Dan Margalit, Karin Melnick and Andrew Putman. [1]
In 2012 Farb became a fellow of the American Mathematical Society. [2] In 2014 he was an invited speaker at the International Congress of Mathematicians in Seoul, speaking in the section on Topology. [3] He was elected to the American Academy of Arts and Sciences in 2021. [4] In 2024 he was awarded the Leroy P. Steele Prize for Mathematical Exposition. [5]
Farb married Amie Wilkinson, professor of mathematics at the University of Chicago, on December 28, 1996. They are professors in the same department. [7]
William Paul Thurston was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds.
John Willard Milnor is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and the only mathematician to have won the Fields Medal, the Wolf Prize, the Abel Prize and all three Steele prizes.
Elias Menachem Stein was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, where he was a faculty member from 1963 until his death in 2018.
In mathematics, in the subfield of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a certain discrete group corresponding to symmetries of the space.
Nicholas Michael Katz is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. He is currently a professor of Mathematics at Princeton University and an editor of the journal Annals of Mathematics.
Dusa McDuff FRS CorrFRSE is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College.
Robion Cromwell Kirby is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant for classifying the piecewise linear structures on a topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links. Along with his significant mathematical contributions, he has over 50 doctoral students and is the editor of an influential problem list.
David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and former director of the then Mathematical Sciences Research Institute (MSRI), now known as Simons Laufer Mathematical Sciences Institute (SLMath). He served as Director of MSRI from 1997 to 2007, and then again from 2013 to 2022.
Phillip Augustus Griffiths IV is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic geometry and which also touches upon major and distant areas of differential geometry. He also worked on partial differential equations, coauthored with Shiing-Shen Chern, Robert Bryant and Robert Gardner on Exterior Differential Systems.
Joan Sylvia Lyttle Birman 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 research professor emerita at Barnard College, Columbia University, where she has been since 1973.
Anthony W. Knapp is an American mathematician at the State University of New York, Stony Brook working on representation theory, who classified the tempered representations of a semisimple Lie group.
Victor William Guillemin is an American mathematician. He works at the Massachusetts Institute of Technology in the field of symplectic geometry, and he has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics.
The mathematician Shmuel Aaron Weinberger is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was, from 1994 to 1996, the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, and he is currently the Andrew MacLeish Professor of Mathematics and chair of the Mathematics department at the University of Chicago.
In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed up to continuous deformation. It is of fundamental importance for the study of 3-manifolds via their embedded surfaces and is also studied in algebraic geometry in relation to moduli problems for curves.
Amie Wilkinson is an American mathematician and Professor of Mathematics at the University of Chicago. Her research topics include smooth dynamical systems, ergodic theory, chaos theory, and semisimple Lie groups. Wilkinson, in collaboration with Christian Bonatti and Sylvain Crovisier, partially resolved the twelfth problem on Stephen Smale's list of mathematical problems for the 21st Century.
Howard Alan Masur is an American mathematician who works on topology, geometry, and combinatorial group theory.
In mathematics, the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed curves on S. The curve complex turned out to be a fundamental tool in the study of the geometry of the Teichmüller space, of mapping class groups and of Kleinian groups. It was introduced by W.J.Harvey in 1978.
In the mathematical subject of geometric group theory, the Švarc–Milnor lemma is a statement which says that a group , equipped with a "nice" discrete isometric action on a metric space , is quasi-isometric to .
Dietmar Arno Salamon is a German mathematician.
Dan Margalit is an American mathematician at Vanderbilt University. His research fields include geometric group theory and low-dimensional topology, with a particular focus on mapping class groups of surfaces.
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