Algebraic and Geometric Combinatorics of Reflection Groups
(Spring School / Workshop)


Picture: A polytopal realization of the associahedron of
     type H3
Algebraic and Geometric Combinatorics of Reflection Groups
(Spring School and Workshop), part of the "Winter 2017 thematic session of the Centre de Recherches Mathématiques (Montréal), with the participation of LaCIM (Laboratoire de Combinatoire et Informatique Mathématique) at UQAM

Montréal, Québec
May 29 to June 9, 2017
  • May 29-June 2, 2017 (Spring school)
  • June 5-June 9, 2017 (Workshop)

This meeting will lie at the interface between algebraic and geometric combinatorial aspects of Coxeter groups and reflection groups. Reflection groups appear in very many domains of mathematics, for instance,

  • as symmetry groups of regular polytopes
  • as quotient of Artin-Tits (braid) groups
  • via root systems, as Weyl groups of semi-simple Lie algebras, Lie groups, algebraic groups, Kac-Moody algebras or cluster algebras and
  • as discrete reflection groups in geometric group theory.
Properties of these groups, finite or infinite, are often key to the understanding of related structures. This conference is concerned with bringing leading experts (and their students and postdocs) to discuss the state of the art in these strongly interconnected and lively areas.
The conference timeline is the following:

  • May 29-June 2 (Spring school):
    Monday May 29 will be devoted to introductory lectures, for interested participants, on common background assumed for the school.
    Picture: The (2,3,7)-triangle group in the Poincaré disc model The main part of the school (May 30-June 2) will consist of four mini-courses.
  • June 5-June 9 (Workshop): There will be twenty talks of one hour duration (including time for questions), four per day, in areas including but not limited to the themes of the previous week's Spring School. Picture: Combinatorial structure of triangular union of chambers of maximal area for the (2,3,7)-triangle group

    For further information, please contact



Monday May 29 will be devoted to introductory lectures, for interested participants, on common background assumed for the school (Humphreys ''Introduction to Coxeter groups and reflection groups'' Chapters 1,2,5,6).

The program for Tuesday May 30 to Friday June 2 will consist of four mini-courses. Each minicourse will consist of four hours of lectures spread over two 2-hour sessions on consecutive days. After the first two hour lecture on day one of each minicourse, a handout with problems and exercises will be given to the attendees for discussion at the beginning of that minicourse's second lecture.

The speakers will be

  • Cédric Bonnafé (CNRS/Université de Montpellier)
  • Piotr Przytycki (McGill University)
  • Nathan Reading (North Carolina State University) and
  • Vic Reiner (University of Minnesota).

Picture: Accumulation of roots in an infinite Coxeter


The workshop on June 5 to June 9 will consist of a program of twenty talks. There will be four one-hour lectures per day, with talks from 9h30 to 11h30 (two talks) and 16h to 18h (two talks). Other time is left free for discussions between conference attendees, and rooms will be available to facilitate such discussions.

Speakers will include:

  • Cédric Bonnafé (CNRS/Université de Montpellier)
  • Sara Billey (U. Washington)
  • Maria Chlouveraki (U. Versailles)
  • Patricia Hersh (North Carolina State U.)
  • Kasia Jankiewicz (McGill U.)
  • Martina Lanini (U. Edinburgh)
  • Gunter Malle* (Technische U., Kaiserslautern)
  • Timothée Marquis (Université catholique de Louvain)
  • Jon McCammond (U.C. Santa Brabara)
  • Karola Mészáros (Cornell U.)
  • Yuya Mizuno* (Nagoya U.)
  • Piotr Przytycki (McGill U.)
  • Nathan Reading (North Carolina State U.)
  • Vic Reiner (U. Minnesota)
  • Vivien Ripoll* (U. Vienne)
  • Salvatore Stella (U. Roma)
  • Nathan Williams (UCSB)
  • Lauren Williams* (Berkeley)
  • (*: To be confirmed.)



    Sara Billey U. Washington
    Cédric Bonnafé Université de Montpelier
    Maria Chlouveraki U. Versaille
    Matthew Dyer University of Notre Dame
    Patricia Hersh North Carolina State U.
    Christophe Hohlweg UQAM
    Kasia Jankiewicz McGill U.
    Martina Lanini U. Edinburgh
    Gunter Malle* Technische U., Kaiserslautern
    Timothée Marquis Université catholique de Louvain
    Jon McCammond U.C. Santa Brabara
    Karola Mészáros Cornell U.
    Yuya Mizuno* Nagoya U.
    Vincent Pilaud LIX, CNRS & École Polytechnique, Paris (Palaiseau)
    Piotr Przytycki McGill U.
    Nathan Reading North Carolina State U.
    Vic Reiner U. Minnesota
    Vivien Ripoll* U. Vienne
    Salvatore Stella U. Roma
    Hugh Thomas UQAM
    Nathan Williams UCSB
    Lauren Williams* Berkeley


    • Reception TBA
    • Minicourses: TBA
    • Workshop: TBA

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    Information on hotels will be coming later.


    Plane:Montreal is served by the Pierre Elliott Trudeau Airport (YUL). From the airport, a taxi to the downtown core costs about $35-$45. More economically, you can take the Airport Express bus #747, which operates 24 hours per day and costs $10 (exact fare necessary coins only! if purchased on bus). However, you can buy a pass by credit card in the airport (see the section Purchasing transit fares at the airport at Airport shuttle.) The ticket is also a transit pass valid during 24h for all the STM network. The closest stop to UQAM is stop number 8 (René Lévesque and Jeanne-Mance)
    Bus:Buses arrive and depart from the Station Centrale d'autobus, which is a short walk to/from UQAM. Intercity bus service is offered by Megabus, Coach Canada, Adirondack Trailways, Greyhound.
    Train:Trains arrive and depart from the Gare Centrale, which is a short walk to/from UQAM. Train service is provided by Via Rail Canada and Amtrak.
    Other:More information can be found on the WikiTravel website for Montreal.

    Other information

    Funding: We are grateful for financial support from the CRM and LaCIM.

    Past conferences: Coxeter groups meet convex geometry (2012).

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