Marc Edward Culler, born November 22, 1953, is an American mathematician recognized for contributions to geometric group theory and low-dimensional topology. A native of California, he completed his undergraduate studies at the University of California at Santa Barbara before earning his graduate degree from the University of California, Berkeley in 1978. He is currently a professor emeritus at the University of Illinois Chicago.
Academic Contributions and Geometry
Culler specializes in 3-manifolds and hyperbolic geometry. Much of his career features collaborations with Peter Shalen, with whom he co-authored numerous research papers. Their joint efforts linked the properties of representation varieties of hyperbolic 3-manifold groups to manifold decompositions. His 1994 paper, "Plane curves associated to character varieties of 3-manifolds," introduced the A-polynomial for knots and 3-manifolds possessing a single torus boundary component.
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Take the IQ test →The Culler–Vogtmann Outer Space
In 1986, Culler published "Moduli of graphs and automorphisms of free groups" alongside Karen Vogtmann. This research introduced a mathematical object that subsequently became known as Culler–Vogtmann Outer space. This concept remains an important element in the study of automorphisms of free groups and continues to influence research within the field of geometric group theory.
Professional Recognition and Service
Culler has served in various capacities within the academic community, including his role as an editor for The New York Journal of Mathematics. His research has been supported by a Sloan Foundation Research Fellowship held between 1986 and 1988. He was designated a UIC University Scholar in 2008 and achieved the status of Fellow of the American Mathematical Society in 2014, maintaining his membership with the organization throughout his career.
Fast facts
- Born: November 22, 1953
- Undergraduate: University of California at Santa Barbara
- Graduate: University of California, Berkeley (1978)
- Primary Fields: Topology, geometric group theory
- Notable Concept: Culler–Vogtmann Outer space
- Awards: Sloan Fellowship, Fellow of the American Mathematical Society (2014)
- Affiliation: University of Illinois Chicago
Questions readers ask
What is the Culler–Vogtmann Outer space?
It is a mathematical object introduced by Marc Culler and Karen Vogtmann in their 1986 paper regarding moduli of graphs and automorphisms of free groups.
With whom has Marc Culler frequently collaborated?
He has frequently collaborated with mathematician Peter Shalen on research concerning the representation varieties of hyperbolic 3-manifold groups.
Achievements
- Held posts at University of Illinois Chicago
- Fields: topology
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