Nathan Michael Dunfield (born 1975) is an American mathematician, specializing in

Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

Career

Dunfield did his undergraduate studies at

Oregon State University Oregon State University (OSU) is a public land-grant, research university in Corvallis, Oregon. OSU offers more than 200 undergraduate-degree programs along with a variety of graduate and doctoral degrees. It has the 10th largest engineering c ...

, obtaining a

B.S. A Bachelor of Science (BS, BSc, SB, or ScB; from the Latin ') is a bachelor's degree awarded for programs that generally last three to five years. The first university to admit a student to the degree of Bachelor of Science was the University ...

in mathematics in 1994. For his graduate studies he went to the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

, obtaining his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in 1999, with a thesis on ''Cyclic Surgery, Degrees of Maps of Character Curves, and Volume Rigidity for Hyperbolic Manifolds'' written under the supervision of

Peter Shalen Peter B. Shalen (born c. 1946) is an American mathematician, working primarily in low-dimensional topology. He is the "S" in JSJ decomposition. Life He graduated from Stuyvesant High School in 1962, and went on to earn a B.A. from Harvard Coll ...

and Melvin Rothenberg. He then was a Benjamin Peirce Assistant Professor at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

(1999–2003) and an associate professor at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

(2003–2007), after which he moved to the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univer ...

, where he was promoted to professor in 2018.

Work

Dunfield is an expert in

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

three-manifolds In mathematics, a 3-manifold is a space (mathematics), space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (geometry), plane to a sma ...

, and

computational Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An espe ...

aspects of these fields. He is also, with

Marc Culler Marc Edward Culler (born November 22, 1953) is an American mathematician who works in geometric group theory and low-dimensional topology. A native Californian, Culler did his undergraduate work at the University of California at Santa Barbara and ...

, one of the key developers of the program SnapPy, the modern version of Jeffrey Weeks' program

SnapPea SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version as part of his doctoral thesis, supervised ...

. Dunfield is an editor for the '' New York Journal of Mathematics''.New York Journal of Mathematics
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Selected publications

* Dunfield, Nathan; Gukov, Sergei; Rasmussen, Jake; ''The superpolynomial for knot homologies.''

Experimental Mathematics Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with th ...

15 (2006), 129–159. math.GT/0505662. * Dunfield, Nathan; Calegari, Danny; ''Laminations and groups of homeomorphisms of the circle.'' Inventiones Mathematicae 152 (2003) 149–207. math.GT/0203192. * Dunfield, Nathan; ''Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds.'' Inventiones Mathematicae 136 (1999) 3, 623–657. math.GT/9802022.

References

External links

* * {{DEFAULTSORT:Dunfield, Nathan 21st-century American mathematicians Topologists Sloan Research Fellows 1975 births Living people Fellows of the American Mathematical Society Institute for Advanced Study visiting scholars Mathematicians from Michigan People from Ann Arbor, Michigan Oregon State University alumni University of Chicago alumni California Institute of Technology faculty Harvard University faculty University of Illinois Urbana-Champaign faculty