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 University Country Number of collaborations
Dror Bar-Natan University of Toronto Canada 5
Gaetan Borot Max Planck Institute for Mathematics, Bonn Germany 1
Jean Bellissard Georgia Institute of Technology USA 1
Ovidiu Costin Ohio State University USA 3
Tudor Dimofte Institute of Advanced Studies, Princeton USA 1
Jerome Dubois Universite Paris VII France 1
Nathan Dunfield University of Illinois Urbana-Champain USA 3
Jeff Geronimo Georgia Institute of Technology USA 1
Matthias Goerner USA 2
Mikhal Goussarov POMI, St. Peterburg Russia 1
Nathan Habegger University of Nantes France 1
Andrei Kapaev Russia 1
Craig Hodgson University of Melbourne Australia 1
Rinat Kashaev University of Geneva Switzerland 1
Christoph Koutschan Johannes Kepler University Austria 4
Andrew Kricker National University of Singapore Singapore 3
Alexander Its Indiana University-Purdue University USA 1
Yueheng Lan Georgia Institute of Technology USA 1
Thang T.Q. Le Georgia Institute of Technology USA 7
Jerome Levine Brandeis University USA 8
Martin Loebl Charles University, Prague Czech Republic 2
Marcos Marino University of Geneve Switzerland 3
Thomas Mattman California State University USA 1
Iain Moffatt University of South Alabama USA 1
Hugh Morton University of Liverpool UK 1
Hiroaki Nakamura Tokyo Metropolitan University Japan 1
Sergey Norin McGill Canada 2
Tomotada Ohtsuki Research Institute for Mathematical Sciences, Kyoto Japan 2
Michael Polyak Tel-Aviv University Israel 1
Ionel Popescu Georgia Institute of Technology USA 1
James Pommersheim Reed College USA 2
Lev Rozansky University of North Carolina USA 5
J. Hyam Rubinstein University of Melbourne Australia 1
Henry Segerman University of Melbourne Australia 1
Alexander Shumakovitch George Washington University, Washington DC USA 1
Xinyu Sun Tulane University USA 3
Peter Teichner Max Planck Institute for mathematics, Bonn Germany 1
Morwen Thislethwaite University of Tennessee, Knoxville USA 1
Dylan P. Thurston Barnard College, New York USA 5
Roland van der Veen University of Amsterdam The Netherlands 3
Thao Vuong Georgia Institute of Technology USA 4
Doron Zeilberger Rutgers University USA 1
Christian Zickert University of California Berkeley USA 4

Ph.D. students
Name University Country
Ian Moffatt University of South Alabama 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