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


  • Geometrical methods in mathematical physics
  • Lie theory and differential equations
  • Classical and quantum integrable systems
  • Algebraic methods in dynamical systems and chaos
  • Exactly and quasi-exactly solvable models
  • Lie groups and algebras, representation theory
  • Orthogonal polynomials and special functions
  • Integrable probability and stochastic processes
  • Quantum algebras, quantum groups and their representations
  • Metric and Riemannian geometry
  • Symplectic, Poisson and noncommutative geometry
  • Algebraic geometry and its applications
  • Quantum field theories and string/gauge theories
  • Statistical physics and condensed matter physics
  • Quantum gravity and cosmology

SIGMA is a refereed purely electronic arXiv overlay journal with a lot of mirrors around the world. In spite of being open access, the journal does not charge authors for publication.

The journal was founded on a volunteer basis in 2005 at the Institute of Mathematics of the NAS of Ukraine by the following people: Vyacheslav Boyko, Anatoly Nikitin, Roman Popovych, Iryna Yehorchenko and Alexander Zhalij.

Currently SIGMA is operated by:

Managing Editors: Vyacheslav Boyko and Alexander Zhalij

Executive Assistant: Vira Pobyzh

Copy-editors: Tetiana Koshuba, Vira Pobyzh, Galyna Popovych, Sofiia Tryhubenko

Editorial Board

Andrei Agrachev (SISSA, Italy)
Paolo Aschieri (University Piemonte Orientale, Alessandria, Italy)
Jinho Baik (University of Michigan, USA)
Glenn Barnich (Université Libre de Bruxelles, Belgium)
Martin Bojowald (Pennsylvania State University, USA)
Richard Borcherds (University of California, Berkeley, USA)
Ivan Corwin (Columbia University, USA)
Eric D'Hoker (University of California, Los Angeles, USA)
Robbert Dijkgraaf (University of Amsterdam, The Netherlands and Institute for Advanced Study, Princeton, USA)
Michael Eastwood (Australian National University, Canberra, Australia)
Bertrand Eynard (Université Paris Saclay, France)
Sergey Fomin (University of Michigan, USA)
Allan Fordy (University of Leeds, UK)
Jürgen Fuchs (Karlstad University, Sweden)
Rod Gover (University of Auckland, New Zealand)
Razvan Gurau (Ecole Polytechnique, France and Universität Heidelberg, Germany)
Johannes Huebschmann (Université des Sciences et Technologies de Lille, France)
Alexander Its (Indiana University - Purdue University Indianapolis, USA)
Niky Kamran (McGill University, Montreal, Canada)
Rinat Kashaev (University of Geneva, Switzerland)
Boris Khesin (University of Toronto, Canada)
Anatol Kirillov (Kyoto University, Japan)
Nikolai Kitanine (Université de Bourgogne, France)
Erik Koelink (Radboud University Nijmegen, The Netherlands)
Tom Koornwinder (University of Amsterdam, The Netherlands)
Yvette Kosmann-Schwarzbach (École Polytechnique, France)
Dirk Kreimer (Humboldt-Universität zu Berlin, Germany)
Arno Kuijlaars (Katholieke Universiteit Leuven, Belgium)
Giovanni Landi (University of Trieste, Italy)
Joseph Landsberg (Texas A&M University, USA)
Claude LeBrun (Stony Brook University, USA)
Eugene Lerman (University of Illinois at Urbana-Champaign, USA)
Roberto Longo (University of Rome Tor Vergata, Italy)
Jerzy Lukierski (University of Wroclaw, Poland)
Lionel Mason (University of Oxford, UK)
Peter D. Miller (University of Michigan, USA)
Andrei Moroianu (Université Paris-Sud, France)
Karl-Hermann Neeb (University of Erlangen-Nürnberg, Germany)
Anatoly Nikitin (Institute of Mathematics of the NAS of Ukraine, Kyiv, Ukraine)
Grigori Olshanski (Institute for Information Transmission Problems)
Peter Olver (University of Minnesota, Minneapolis, USA)
Eric Opdam (University of Amsterdam, The Netherlands)
Roman Popovych (Silesian University in Opava, Czech Republic and Institute of Mathematics of the NAS of Ukraine, Kyiv, Ukraine)
Eric M. Rains (California Institute of Technology, 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)
Hubert Saleur (Université Paris Saclay, France and University of Southern California, USA)
Carlos Simpson (Université de Nice - Sophia Antipolis, France)
Christina Sormani (City University of New York, USA)
Jasper Stokman (University of Amsterdam, The Netherlands)
Ross Street (Macquarie University, Australia)
Yuri Suris (Technische Universität Berlin, Germany)
Richard Szabo (Heriot-Watt University, Edinburgh, UK)
Kanehisa Takasaki (Kinki University, Japan)
Arkady Tseytlin (Imperial College London, UK)
Walter Van Assche (University of Leuven, Belgium)
Alexander Varchenko (University of North Carolina at Chapel Hill, USA)
Erik Verlinde (University of Amsterdam, The Netherlands)
Alexander Veselov (Loughborough University, UK)
Alan Weinstein (University of California, Berkeley, USA)
Christopher Woodward (Rutgers University, USA)

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

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

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

If the receipt of your paper is not acknowledged within two working days, please resend it to our alternative e-mail address

The length of an article is not limited.

We are accepting only two submissions per author, per year. In some cases, this limit may be exceeded if an article is submitted at the personal invitation of the editors or guest editors.

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. However, in spite of being 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 a 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 two experts in the specific areas for evaluation according to the above criteria. These referees can either review the papers themselves or recommend alternative referee(s).

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

  • we do not involve as referees people that were co-authors of any of the paper's authors in the recent years;
  • a referee of a paper should not be a co-author of another referee of the same paper in the recent years.

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 amended according to the referees' recommendations.

We do our best to keep track of and rule out any possibility for conflicts of interest in the selection of the referees. Please inform us if such conflicts arise.

Please contact the Editors for further 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. Acceptance 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 a special issue of 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?
SIGMA receives major funding from the Foundation Compositio Mathematica and the University Library of the Radboud University Nijmegen. Also, one-time donations have been received from Sociedad Mexicana de Física, University Libraries of the Delft University of Technology, Uppsala University and University of Amsterdam. It is a great pleasure for SIGMA to acknowledge these. We greatly appreciate also the assistance of EMIS who kindly provides mirrors for SIGMA.

Looking for your support/sponsorship
The above support covers only a part of SIGMA costs. We need money for the support of volunteers doing technical work for SIGMA, including but not limited to the copyediting. So, if your organization would like to support us financially, please contact us.

SIGMA is arXiv overlay journal

This means that, in addition to the freely accessible pdfs and tex-sources on the journal's website and its mirrors, all published articles in the journal are contributed also to the arXiv. In addition, the SIGMA web site has hyperlinks to the arXiv copies. 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 the arXiv, we suggest the authors choose one of the following two ways:

  • We send to the authors zipped tex-source of the journal (published) version of the article, as well as instructions on how to fill in the appropriate fields, and then the authors oneself replace the article in the arXiv with its journal version.

  • Alternatively, SIGMA, as an authorized proxy submitter, can also replace (or submit) an article in the arXiv on behalf of the authors. To do this, we should receive from the authors the paper password. If you have forgotten the paper's password, please use the paper password recovery form.

If the authors want to make changes to an already published article (i.e. make a corrigendum), we publish a new version of the article on the journal's website (please see an example) and replace the article in the arXiv. In the case of minor changes (when referees are not needed), we do it quite quickly, in a few days.

Indexing & Abstracting

SIGMA is covered by the following indexing and abstracting databases:

Copyright Issues

The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License .

Back to the SIGMA main page.