Stavros Garoufalidis

Professor Department of Mathematics

Personal Profile

Professor Stavros Garoufalidis: born in May 1965, started to work in 1992; Nationality: United States, Greece; Language: Greek, English, French.

Professor, Southern University of Science and Technology 2019-present

External Scientific Member, Max Planck Institute for Mathematics 2019-present

Hirzebruch Research Chair, Max Planck Institute for Mathematics 2018-19

Professor, Georgia Institute of Technology 2003-19

Associate Professor, Georgia Institute of Technology 2001-02

Lecturer, University of Warwick 2001-02

Assistant Professor, Georgia Institute of Technology 1999-00

Assistant Professor, Harvard University 1998-99

Assistant Professor, Brandeis University 1997-98

Assistant Professor, Harvard University 1996-97

Tamarkin Instructor, Brown University 1995-96

CLE Moore Instructor, MIT 1993-95

MSRI member 1992-93


Quantum topology and mathematical physics.


Linear algebra

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Stavros got interested in TQFT (topological quantum field theory) invariants of knotted 3-dimensional objects, such as knots, braids, srting-links or 3-manifolds in his early career.

Later on, he became interested in finite type invariants (a code name for perturbative quantum field theory invariants of knotted objects). He studied their axiomatic properties, and related the various definitions to each other. A side project was to study the various filtrations of the mapping class groups, and to explicitly construct cocycles, using finite type invariants.

More recently, he has been studying the colored Jones polynomials of a knot, and its limiting geometry and topology. The colored Jones polynomials is not a single polynomial, but a sequence of them, which is known to satisfy a linear q-difference equation. Writing the equation into an operator form, and setting q=1, conjecturally recovers the A-polynomial. The latter parametrizes out the moduli space of SL(2,C) representation of the knot complement.

Another relation between the colored Jones polynomial and SL(2,C) (ie, hyperbolic) geometry is the Volume Conjecture that relates evaluations of the colored Jones polynomial to the volume of a knot. This and related conjectures fall into the problem of proving the existence of asymptotic expansions of combinatorial invariants of knotted objects. Most recently, he is working on resurgence of formal power series of knotted objects. Resuregence is a key property which (together the nonvanishing of some Stokes constant) implies the Volume Conjecture. Resurgence is intimately related to Chern-Simons perturbation theory, and produces singularities of geometric as well as arithmetic interst. Resurgence seems to be related to the Grothendieck-Teichmuller group.

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