The Reflection Groups Network aims to create a space for exchange between researchers from all areas of mathematics in which the concept of groups with mirror symmetries naturally occurs.

Reflection groups and Coxeter groups can be approached from algebraic, geometric, topological and combinatorial perspectives. They are deeply intertwined with a wide range of natural algebraic, combinatorial and geometric structures and play a central role across many areas of mathematics. Instances of the appearence of reflection groups include:

  • Weyl groups in Lie theory, representation theory and Cluster algebras via root systems,
  • symmetry groups of regular and abstract polytopes,
  • discrete reflection groups,
  • (quotients of) Artin–Tits (braid) groups,
  • examples of non-positively curved (CAT(0)) groups,
  • arithmetic reflection groups defined over number fields.
  • abstractly defined cousins with similar presentations, e.g. Dyer groups

Understanding the properties of these groups, whether finite or infinite, is often key to understanding the structures built upon them. The variety of contexts in which they appear naturally invites a diversity of techniques and viewpoints.

Mission

We aim to bring together researchers from these strongly interconnected and vibrant areas, fostering exchange on recent developments and shared perspectives on common structures through:

  • the RGN online seminar;
  • the organization of an annual event like a workshop, a school or a conference (labelled ‘RGN-event’ on this site);
  • promote scientific events in relation to the RGN aim.

RGN is an inclusive network, the above subjects are mentioned for information. Please contact us to inform us of any subject with a flavour of reflection groups or mirror symmetries.

The RGN is born out of discussions in 2012 between Matthew Dyer, Christophe Hohlweg and Vincent Pilaud.

Contact

To contact us (to advertise your event on the RGN webpage, to organize an event with the RGN, …), please write to reflectiongroupsnetwork(at)mathi(dot)uni-heidelberg(dot)de

Steering committee

  • Christophe Hohlweg
    Département de mathématiques – LACIM, Université du Québec à Montréal, Québec, Canada

  • Martina Lanini
    Università di Roma Tor Vergata, Dipartimento di Matematica, Italy

  • Vincent Pilaud
    Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Spain

  • Petra Schwer
    Heidelberg University, Institute for Mathematics, Germany