Stavros Garoufalidis

Southern University of Science and Technology
International Center for Mathematics
201 Jinqizhigu Building, No.4 Chongwen Garden
No.1 Tangling Road, Nanshan District
Shenzhen, Guangdong Province, 518055 CHINA
Phone: +86 07552692 4295 ext 8057

External Scientific Member
Max-Planck-Institute for Mathematics
Vivatsgasse 7, 53111 Bonn, GERMANY
Phone: +49-228-402-0


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 (66)
Name Place Country
Joergen Ellegaard Andersen University of Southern Denmark Denmark
Dror Bar-Natan University of Toronto Canada
Jean Bellissard Georgia Institute of Technology USA
Jennifer Brown University of California Davis USA
Frank Calegari The University of Chicago USA
Ovidiu Costin Ohio State University USA
Zsuzsanna Dancso Australian National University, Canberra Australia
Renaud Detcherry University of Dijon, Dijon France
Tudor Dimofte The University of Edinburgh UK
Jerome Dubois Universite Paris VII France
Zhihao Duan KIAS, Seoul South Korea
Nathan Dunfield University of Illinois Urbana-Champain USA
Evgeny Fominykh Chelyabinsk State University, Chelyabinsk Russia
Nathan Geer Utah State University USA
Jeff Geronimo Georgia Institute of Technology USA
Matthias Goerner Pixar Animation Studios USA
Mikhal Goussarov POMI, St. Peterburg Russia
Jie Gu Southeast University, Nanjing China
Nathan Habegger University of Nantes France
Andrei Kapaev International School for Advanced Studies, Trieste Italy
Craig Hodgson University of Melbourne Australia
Neil Hoffman Oklahoma State university, Stillwater USA
Rinat Kashaev University of Geneva Switzerland
Christoph Koutschan Johannes Kepler University Austria
Andrew Kricker National University of Singapore Singapore
Piotr Kucharski University of Warsaw, Warsaw Poland
Alexander Its Indiana University-Purdue University USA
BoGwang Jeon Pohang University of Science and Technology Korea
Yueheng Lan Georgia Institute of Technology USA
Aaron Lauda University of Southern California USA
Thang T.Q. Le Georgia Institute of Technology USA
Christine Lee University of South Alabama 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 London UK
Hugh Morton University of Liverpool UK
Sameer Murthy Kings College, London UK
Hiroaki Nakamura Tokyo Metropolitan University Japan
Sergey Norin McGill University 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
Emanuel Scheidegger Peking University China
Henry Segerman Oklahoma State University USA
Alexander Shumakovitch George Washington University, Washington DC USA
Matthias Storzer Max-Planck-Institute-for-Mathematics, Bonn Germany
Piotr Sulkowski University of Warsaw, Warsaw Poland
Xinyu Sun Tulane University USA
Vladimir 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 University of Indiana, Bloomington USA
Roland van der Veen University of Groningen The Netherlands
Andrei Vesnin Sobolev Institute of Mathematics, Novosibirsk Russia
Thao Vuong Georgia Institute of Technology USA
Campbell Wheeler IHES, Paris France
Seokbeom Yoon International Center for Mathematics, SUSTech China
Tao Yu International Center for Mathematics, SUSTech China
Doron Zeilberger Rutgers University USA
Don Zagier Max Planck Institute, Bonn Germany
Christian Zickert University of Maryland USA

Ph.D. students
Name Place Country
Campbell Wheeler MPIM/University of Bonn Germany
Ian Moffatt University of London UK
Roland van der Veen University of Amsterdam The Netherlands
Thao Vuong Georgia Institute of Technology USA

Submission to the Journal of Knot Theory and its Ramifications

A list of seminars in the MPIM and Bonn.