Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


  • Geometrical methods in mathematical physics
  • Lie theory and differential equations
  • Classical and quantum integrable systems
  • Dynamical systems and chaos
  • Exactly and quasi-exactly solvable models
  • Lie groups and algebras, representation theory
  • Orthogonal polynomials and special functions
  • Quantum algebras, quantum groups and noncommutative geometry
  • Supersymmetry and supergravity, strings and branes
  • Cosmology and quantum gravity

SIGMA is a refereed purely electronic arXiv overlay journal with a lot of mirrors around the world. Despite being open access, the journal does not charge authors for publication. SIGMA is a non-profit, volunteer-run project operated by the following people (all from the Institute of Mathematics of NAS of Ukraine):

Editor: Anatoly Nikitin

Associate Editors: Vyacheslav Boyko, Roman Popovych, Iryna Yehorchenko, Alexander Zhalij

Executive Assistant: Vira Pobyzh

Editorial Board

Mark Ablowitz (University of Colorado, USA)
Mark Adler (Brandeis University, USA)
Alexander Andrianov (Saint Petersburg State University, Russia)
Paolo Aschieri (E. Fermi Centre, Rome and University Piemonte Orientale, Alessandria, Italy)
Glenn Barnich (Université Libre de Bruxelles, Belgium)
Martin Bojowald (Pennsylvania State University, USA)
Richard Borcherds (University of California, Berkeley, USA)
Francesco Calogero (University of Rome "La Sapienza", Italy)
James Carlson (Clay Mathematics Institute and University of Utah, USA)
Peter Clarkson (University of Kent at Canterbury, UK)
Edward Corrigan (University of York, UK)
Thomas Curtright (University of Miami, USA)
Robbert Dijkgraaf (University of Amsterdam, The Netherlands and Institute for Advanced Study, Princeton, USA)
Boris Dubrovin (International School for Advanced Studies (SISSA), Trieste, Italy)
Charles Dunkl (University of Virginia, USA)
Michael Eastwood (Australian National University, Canberra, Australia)
László Fehér (Research Institute for Particle and Nuclear Physics, Budapest and University of Szeged, Hungary)
Athanassios Fokas (University of Cambridge, UK)
Allan Fordy (University of Leeds, UK)
Stavros Garoufalidis (Georgia Institute of Technology, Atlanta, USA)
Rod Gover (University of Auckland, New Zealand)
Basile Grammaticos (Université Paris VII, France)
Harald Grosse (University of Vienna, Austria)
Darryl D. Holm (Imperial College London, UK)
Johannes Huebschmann (Université des Sciences et Technologies de Lille, France)
Jacques Hurtubise (McGill University, Montreal, Canada)
Niky Kamran (McGill University, Montreal, Canada)
Boris Khesin (University of Toronto, Canada)
Evgueni Khruslov (Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine)
Anatol Kirillov (Kyoto University, Japan)
Erik Koelink (Radboud University Nijmegen, The Netherlands)
Tom Koornwinder (University of Amsterdam, The Netherlands)
Yvette Kosmann-Schwarzbach (École Polytechnique, France)
Alan Kostelecky (Indiana University, USA)
Dirk Kreimer (Humboldt-Universität zu Berlin, Germany)
Igor Krichever (Columbia University, USA)
Petr Kulish (Petersburg Department of Steklov Institute of Mathematics, St.Petersburg, Russia)
Giovanni Landi (University of Trieste, Italy)
Claude LeBrun (Stony Brook University, USA)
Roberto Longo (University of Rome Tor Vergata, Italy)
Eugene Lerman (University of Illinois at Urbana-Champaign, USA)
Jerzy Lukierski (University of Wroclaw, Poland)
Kirill C.H. Mackenzie (University of Sheffield, UK)
Robert Mann (University of Waterloo, Canada)
Lionel Mason (University of Oxford, UK)
Alexander Mikhailov (University of Leeds, UK)
Willard Miller, Jr. (University of Minnesota, Minneapolis, USA)
Robert Minlos (Institute for Information Transmission Problems, Moscow, Russia)
Richard Montgomery (The University of California, Santa Cruz, USA)
Robert Moody (University of Victoria, Victoria, Canada)
Mikhail Olshanetsky (Institute of Theoretical and Experimental Physics, Moscow, Russia)
Grigori Olshanski (Institute for Information Transmission Problems, Moscow, Russia)
Peter Olver (University of Minnesota, Minneapolis, USA)
Jiri Patera (Centre de Recherches Mathematiques, Montreal, Canada)
Orlando Ragnisco (Universita di Roma 3, Italy)
Pierre Ramond (University of Florida, USA)
Tudor Ratiu (Ecole Polytechnique Fédérale de Lausanne, Switzerland)
Jonathan Rosenberg (University of Maryland, USA)
Carlo Rovelli (Centre de Physique Theorique de Luminy, Marseille, France)
Simon Ruijsenaars (University of Leeds, UK)
Vadim Schechtman (Université Paul Sabatier, Toulouse, France)
Israel Michael Sigal (University of Toronto, Canada)
Andrei Smilga (Universite de Nantes, France)
Alexei Starobinsky (Landau Institute of Theoretical Physics, Moscow, Russia)
Daniel Sternheimer (Universite de Bourgogne, Dijon, France and Rikkyo University, Tokyo, Japan)
Jasper Stokman (University of Amsterdam, The Netherlands)
Yuri Suris (Technische Universität Berlin, Germany)
Richard Szabo (Heriot-Watt University, Edinburgh, UK)
Kanehisa Takasaki (Kinki University, Japan)
Arkady Tseytlin (Imperial College London, UK and Lebedev Institute, Moscow, Russia)
Alexander Varchenko (University of North Carolina at Chapel Hill, USA)
Erik Verlinde (University of Amsterdam, The Netherlands)
Alan Weinstein (University of California, Berkeley, USA)
Pavel Winternitz (Centre de Recherches Mathematiques, Montreal, Canada)

Authors who wish to have their manuscript handled by a specific member of the Editorial Board should notify the Editorial Office (about this) at the time of submission.

How to Submit an Article

Please submit the paper to and send the arXive number to or (only in exceptional cases) you can send the zipped paper in TeX/LaTeX format directly to (please include the PDF or PostScript file as well) with explanation why you prefer not to put the paper to arXiv.

Your article may be prepared for submission in any TeX-style of your choice. Though we would like to point out that after the paper is accepted for publication you should prepare the paper in accordance to the SIGMA style (which can be downloaded from here).

Please indicate in your submission if your paper is intended for a specific special issue of SIGMA.

If you do not receive a confirmation within two working days that we have received your paper, please resend it to our alternative address

The length of an article is not limited.

We are accepting only two submissions per author, per year.

The average time of the paper processing (from the submission of the paper to its appearance on the journal's web site) is 2–4 months. However, this essentially depends on the subject and the length of the article, so in some cases the processing can take longer.

The papers are considered for publication if they have not been published previously and are not submitted for publication elsewhere.

SIGMA is an open access journal. Nevertheless, despite open access, the journal charges no publication fees (i.e., it is no-fee open-access journal).

Paper Evaluation Criteria

SIGMA has two article styles: regular article and review article.

Manuscripts submitted as regular articles are expected to be
- new and original;
- well organized and clearly written;
- of interest to the scientific community;
- not published previously and not under consideration for publication in any other journal or book.

Review articles are welcome too. Review articles are critical evaluations of material that has already been published. By organizing, integrating and evaluating previously published material, the author of a review article considers the progress of current research toward clarifying a problem. In a sense, a review article is tutorial in that the author
- defines and clarifies the problem;
- summarizes previous investigations in order to inform the reader of the state of current research;
- identifies relations, contradictions, gaps, and inconsistencies in the literature;
- and suggests a next step or steps in solving the problem.

Refereeing Papers for SIGMA

All the papers submitted to SIGMA are sent for refereeing to at least 2 experts in the specific areas for evaluation according to the above criteria. These referees can either review the papers themselves or recommend other referee(s).

To ensure comprehensive refereeing and to avoid conflicts of interest we choose the referees having in mind:

  • not to involve as referees people that were co-authors of any of the paper's author in the recent years; moreover, we try to ensure that a referee and an author of the paper are not co-authors of the same person.
  • a referee of a paper should not be a co-author of another referee of the same paper in the recent years; moreover, we try to ensure that the referees of the paper are not co-authors of the same person.

We strive to ensure an adequate refereeing and selection process. At the moment around 60 percent of the submitted papers are rejected. Most of the accepted papers have been corrected in accordance with the referees' recommendations.

We monitor any possibility for conflicts of interest in the selection of the referees. Please also inform us if such conflicts arise.

Please contact the Editors for questions about the editorial process and our refereeing policy.

Special thematic issues in SIGMA

SIGMA welcomes proposals from potential Guest Editors for special thematic issues of the journal.

We would like to stress that all papers in the special issues should be original: they should not be simply reviews of authors' own work that is already published elsewhere. Acception of the paper is subject to the results of the peer review process according to regular refereeing rules of SIGMA (see the items above).

If you have any ideas for special issue in SIGMA, please contact us for further consideration.

Free for authors, free for readers

Free for readers
This means that SIGMA does not charge its readers for access; it is an open access journal. Papers are available online free of charge and no subscription is needed to read the full text. Commercial publishers actually charge for work done by other people – researchers that produce scientific results, and editors and referees that select the papers. As a result, many scientists cannot afford access to the majority of publications. We believe that such a situation is fundamentally unfair.

Free for authors
Despite being open access, we do not charge our authors for publication (i.e., SIGMA uses the so-called diamond open access model). Many authors submitting good papers cannot afford to pay page charges for various reasons and we do not want to put them at a disadvantage compared to those who can pay. On the other hand, when a journal charges their authors for publication, the requirements of thorough review may contradict financial interests of the journal. This often results in the publication of low-quality papers without adequate peer review and discredits the very idea of open access.

What are the sources for SIGMA existence?
The journal has no revenue and steady sources of funding whatsoever and operates solely on the basis of the good will efforts of its editors. All editorial work, including but not limited to the copyediting, is done by volunteers free of charge. On a regular basis, SIGMA is not supported financially by any entity (organization, foundation, fund, etc.) in Ukraine or abroad, including the National Academy of Sciences of Ukraine. SIGMA is a non-profit, volunteer-run project.
One-time supports have been received from the Foundation Compositio Mathematica, Sociedad Mexicana de Física, and the University Libraries of the Radboud University Nijmegen and Delft University of Technology. It is a great pleasure for SIGMA to acknowledge these supports. We greatly appreciate also the assistance of EMIS who kindly provides mirrors for SIGMA.

Looking for your support/sponsorship
We need money for the web hosting, the CrossRef membership and the support of volunteers doing technical work for SIGMA. So, if you (or your organization) would like to support us financially, please contact us.

SIGMA is arXiv overlay

That means that all published articles in the journal have been contributed or will be contributed to the arXiv. In addition, the SIGMA web site has hyperlinks to the arXiv copies.

You can also search or browse SIGMA articles within the arXiv, for example by following this link. As a consequence of the overlay arrangement, SIGMA shares the commitment of arXiv to remain permanently and freely available on the Internet.

If a paper accepted for publication is already on arXiv, the author should give the Editors both the paper number and the password so that we can replace it with the typeset version.

Indexing & Abstracting

SIGMA is covered by the following indexing and abstracting databases:

Copyright Issues

The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

Back to the SIGMA main page.