Overview

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The CRM has resumed some of its activities that are strictly related to this thematic semester with a limited number of participants.

The following post-doctoral participants are currently in Montreal:

  • Angelica Babei
  • Lea Beneish
  • Antonio Cauchi
  • Lennart Gehrmann
  • Mathilde Gerbelli-Gauthier
  • Debanjana Kundu
  • Jackson Morrow
  • Maria Rosaria Pati
  • Gautier Ponsinet
  • Alice Pozzi
  • Jishnu Ray
  • Joel Specter
  • Salim Tayou

Here is a list of ongoing activities related to the thematic semester, in addition to the four workshops listed on the left:

  • Members seminar
  • Séminaire Quebec-Vermont sur la Théorie des nombres
  • p-adic Galois representations by Adrian Iovita and Giovanni Rosso
  • Modular forms and the theory of complex multiplication by Henri Darmon.
  • Course on modularity lifting by Patrick Allen
  • Preparatory discussion group for Wieslawa Niziol's Aisenstadt lectures and the workshop on higher Coleman theory and its applications.
  • Special semester on Cohomology in Arithmetic, Fall 2020



    Homological tools and ideas are pervasive in number theory. To defend this assertion, it suffices to evoke the role of étale cohomology in the study of the zeta functions of varieties over finite fields through the Weil conjectures, or the cohomological approach to class field theory formulated by Artin and Tate in the 1950's. The theory of motives, a manifestation of a universal cohomology theory attached to algebraic varieties, and the attendant motivic cohomology plays a central role in describing the special values of L-functions of varieties over number fields, via the conjectures of Deligne, Beilinson-Bloch, and Bloch-Kato. Much progress in the Langlands program exploits the fruitful connection between automorphic representations and the cohomology of associated Shimura varieties and more general arithmetic quotients of locally symmetric spaces. The study of special values of L-functions and the Langlands program, widely perceived as two fundamental yet seperate strands of the subject in the early 1990's, were beautifully unified in Wiles' epoch-making proof of the Shimura-Taniyama conjecture, in which this conjecture was reduced to a special instance of the Bloch-Kato conjecture for the symmetric square motive of an elliptic curve. Recent years have seen great strides in our understanding of the cohomology of the arithmetic quotients arising in the study of automorphic representations, spurred in part by the desire to extend the range of applicability of the celebrated Taylor-Wiles method. This has led to new automorphy and potential automorphy results: most spectacularly, perhaps, for abelian surfaces, as well as elliptic curves over general CM fields.

    List of long-term participants

    • Patrick Allen (McGill University), 20 août - 20 décembre
    • Daniel Barrera (Universidad de Santiago de Chile; Simons scholar), 20 septembre - 15 décembre
    • Lea Beneish (CRM-ISM postdoc), 1er août - 20 décembre
    • Denis Benois (Instutut de Mathématiques de Bordeaux; Simons Professor), 2 mois, à venir
    • Nicolas Bergeron (Université Paris 6 et ENS; Aisenstadt Chair), 2 ou 3 semaines vers 19- 23 octobre
    • Ricardo Brasca ((CNRS -International research laboratory), 20 août - 20 décembre
    • Henri Darmon (McGill University) 20 août - 20 décembre
    • Mladen Dimitrov (Université de Lille; Simons Professor), 23 août - 10 décembre
    • Mathilde Gerbelli-Gauthier (CRM-ISM Postdoc), 1er juillet - 20 décembre
    • Eyal Goren (McGill University), 20 août - décembre 20
    • Adrian Iovita (Concordia University), 20 août - 20 décembre
    • Antonio Lei (Université Laval), 20 août - 20 décembre
    • Michael Lipnowksi (McGill University), 20 août - 20 décembre
    • David Loeffler (University of Warwick; Simons Professor), Aug 15 - 15 décembre
    • Adam Logan (Carleton University), 15 septembre - 30 novembre
    • Wieslawa Niziol (École Normale Supérieure de Lyon; Aisenstadt Chair), 11 octobre - 12 décembre
    • Giovanni Rosso (Concordia University), 20 août - décembre
    • Ehud de Shalit (University of Jerusalem; Simons Professor), 23 août - 31 octobre
    • Salim Tayou (CICMA postdoc), 1er septembre - 20 décembre
    • Sarah Zerbes (University College London; Simons Professor), 15 octobre - 15 décembre