About the GAF

What is the GAF?

The Group Action Forum (GAF) is an international mathematical association founded in the year 2002 to form a scientific interdisciplinary forum for mathematicians interested in these branches of mathematics in which transformation groups appear, and the notion of group and the concept of symmetry play important roles.

At the moment, 310 mathematicians have joined the GAF and their institutional affiliations are in 40 countries in total, including: Albania, Armenia, Belarus, Belgium, Brasil, Canada, China, Czech Republic, Denmark, Finland, France, Georgia, Germany, Hungary, India, Iran, Israel, Italy, Japan, México, Morocco, The Netherlands, New Zealand, Norway, Pakistan, Philippines, Poland, Portugal, Republic of Korea, Russia, Serbia and Montenegro,Slovakia, Slovenia, South Africa, Spain, Switzerland, Tunisie, Turkey, United Kingdom, United States of America.

Scientific Focus

The Group Action Forum focuses on appearance of transformation groups in the mathematical sciences, especially in branches of mathematics such as algebra, geometry, topology, analysis, number theory, and mathematical physics. Mathematical interests of GAF Members include areas of pure mathematics such as

  • equivariant algebraic topology
  • Lie group actions on manifolds and cell complexes
  • algebraic group actions on varieties, algebraic quotients
  • geometry of discrete transformation groups, orbifolds
  • Lie group theory and its homotopy theoretic version
  • loop groups and loop spaces
  • algebraic groups and related structures
  • automorphisms of Riemann and Klein surfaces
  • Veech groups
  • translation surfaces (in particular: origamis)
  • algebraic curves in moduli space
  • Teichmueller disks and Teichmueller curves
  • automorphisms of free groups
  • mapping class group
  • L2-invariants and their applications
  • Rigidity theorems for manifolds
  • Klein varieties, higher-dimensional varieties
  • classifying spaces and cohomology of groups
  • group representation theory
  • combinatorial and geometric group theory
  • Coxeter groups, reflection groups, buildings
  • aspherical manifolds and spaces
  • Bieberbach groups, flat manifolds
  • crystallographic groups and topology
  • K-Theory and equivariant K-Theory
  • Galois theory, inverse Galois theory
  • Galois cohomology, Galois representations
  • symmetry methods in nonlinear analysis
  • symmetries of knots, braid groups
  • surgery theory and equivariant surgery theory
  • controlled topology
  • toric topology
  • string topology

Goals and Purposes

The primary aim is to propagate among scientists and students these highly interdisciplinary and very attractive areas of pure mathematics mentioned above. The emphasize is put on the study, development, influence, and application of the theory of transformation groups in the mathematical sciences. More specific goals and purposes are

  • to inform about the history, current trends, and new results
  • to popularize extraordinary achievements and conjectures
  • to organize schools, workshops, and conferences
  • to publish books, text books, and conference proceedings.


For GAF members, there are no costs, duties, or obligations. Once you are a GAF member, you obtain and you can send messages to GAF members, as well as you receive GAF Newsletters. Moreover, you can ask or answer questions by e-mailing to Krzysztof Pawałowski at This email address is being protected from spambots. You need JavaScript enabled to view it. (the GAF Newsletter Editor). In order to keep your experience as spam-free as possible, only GAF members are able to send e-mails to This email address is being protected from spambots. You need JavaScript enabled to view it. to correspond with all GAF members. If you wish to be a GAF member, e-mail to Krzysztof Pawałowski at This email address is being protected from spambots. You need JavaScript enabled to view it. and in your message, please include the following data:

  • your full name (first, middle, last)
  • your full affiliation/correspondence address
  • your e-mail address and URL of your personal web site (if you have one
  • mathematical interests in key words: general areas (e.g. algebraic topology, transformation groups) and specific topics (e.g. group cohomology, group actions on spheres, etc.)

Then you will be added to the GAF Member List located at this web site (please click the Members button). Moreover, you will be provided with the password which enables you to access more information about GAF members. We hope you will join the GAF!