Stavros Garoufalidis
School of Mathematics
Georgia Institute of Technology
Atlanta, Georgia 30332-0160, USA
Phone: (404) 894-6614
 Fax: (404) 894-4409

Email: stavros@math.gatech.edu



Contents

Quantum Topology and Hyperbolic Geometry in Nha Trang, Vietnam May 13-17, 2013
Geometry, Quantum Topology and Asymptotics, Confucius Institute of the University of Geneva, Switzerland June 30-July 5 2014
Curriculum Vitae in pdf

Research Interests

My research interests are in low (i.e. 3 and 4) dimensional topology, the Jones polynomial, hyperbolic geometry, mathematical physics, Chern-Simons theory, string theory, M-theory, enumerative combinatorics, enumerative algebraic geometry, number theory, quantum topology, asymptotic analysis, numerical analysis, integrable systems, motivic cohomology, K-theory, Galois theory, deformation and geometric quantization.

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

Later on, I became interested in finite type invariants (a code name for perturbative quantum field theory invariants of knotted objects). I 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, I have 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, I am 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.

In short, my interests are in low dimensional topology, geometry and mathematical physics.


Collaborators
Name Place Country
Dror Bar-Natan University of Toronto Canada
Jean Bellissard Georgia Institute of Technology USA
Ovidiu Costin Ohio State University USA
Tudor Dimofte Institute of Advanced Studies, Princeton USA
Jerome Dubois Universite Paris VII France
Nathan Dunfield University of Illinois Urbana-Champain USA
Evgeny Fominykh Chelyabinsk State University, Chelyabinsk Russia
Jeff Geronimo Georgia Institute of Technology USA
Matthias Goerner Pixar Animation Studios USA
Mikhal Goussarov POMI, St. Peterburg Russia
Nathan Habegger University of Nantes France
Andrei Kapaev International School for Advanced Studies, Trieste Italy
Craig Hodgson University of Melbourne Australia
Rinat Kashaev University of Geneva Switzerland
Christoph Koutschan Johannes Kepler University Austria
Andrew Kricker National University of Singapore Singapore
Alexander Its Indiana University-Purdue University USA
Yueheng Lan Georgia Institute of Technology USA
Thang T.Q. Le Georgia Institute of Technology USA
Jerome Levine Brandeis University USA
Martin Loebl Charles University, Prague Czech Republic
Marcos Marino University of Geneve Switzerland
Thomas Mattman California State University USA
Iain Moffatt University of South Alabama USA
Hugh Morton University of Liverpool UK
Hiroaki Nakamura Tokyo Metropolitan University Japan
Sergey Norin McGill Canada
Tomotada Ohtsuki Research Institute for Mathematical Sciences, Kyoto Japan
Michael Polyak Tel-Aviv University Israel
Ionel Popescu Georgia Institute of Technology USA
James Pommersheim Reed College USA
Lev Rozansky University of North Carolina USA
J. Hyam Rubinstein University of Melbourne Australia
Henry Segerman University of Melbourne Australia
Alexander Shumakovitch George Washington University, Washington DC USA
Xinyu Sun Tulane University USA
ladimir Tarkaev Chelyabinsk State University, Chelyabinsk Russia
Peter Teichner Max Planck Institute for mathematics, Bonn Germany
Morwen Thislethwaite University of Tennessee, Knoxville USA
Dylan P. Thurston Barnard College, New York USA
Roland van der Veen University of Amsterdam The Netherlands
Andrei Vesnin Sobolev Institute of Mathematics, Novosibirsk Russia
Thao Vuong Georgia Institute of Technology USA
Doron Zeilberger Rutgers University USA
Christian Zickert University of Maryland USA

Ph.D. students
Name Place Country
Ian Moffatt University of London UK
Eric Sabo Georgia Tech, current student USA
Shane Scott Georgia Tech, current student USA
Roland van der Veen University of Amsterdam The Netherlands
Thao Vuong Georgia Institute of Technology USA


Teaching

In the fall of 2014, I am teaching Calculus III (Math 2401) and Point Set Topology (Math 4431)

Submission to the Journal of Knot Theory and its Ramifications


Seminars
A list of seminars in the Math Department, Georgia Tech.

Miscallanea