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. Post-doctoral participants and long-term visitors have been assigned individual offices.

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: Members' seminar

  • Quebec-Vermont Number Theory Seminar
  • Course on Galois representations, by Adrian Iovita and Giovanni Rosso.
  • Course on complex multiplication by Henri Darmon.
  • Course on modularity lifting by Patrick Allen
  • 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), August 20 - December 20
    • Daniel Barrera (Universidad de Santiago de Chile; Simons scholar), September 20 - December 15
    • Lea Beneish (CRM-ISM postdoc), August1-December20
    • Denis Benois (Instutut de Mathématiques de Bordeaux; Simons Professor), 2 months, TBD  
    • Nicolas Bergeron (Université Paris 6 et ENS; Aisenstadt Chair), Two to three weeks around October 19-23
    • Ricardo Brasca ((CNRS -International research laboratory), August 20 - December 20
    • Henri Darmon (McGill University) August 20 - December 20
    • Mladen Dimitrov (Université de Lille; Simons Professor), August 23 - December 10
    • Mathilde Gerbelli-Gauthier (CRM-ISM Postdoc), July 1 - December 20
    • Eyal Goren (McGill University), August 20 - December 20
    • Adrian Iovita (Concordia University), August 20 - December 20
    • Antonio Lei (Université Laval), August 20 - December 20 
    • Michael Lipnowksi (McGill University), August 20 - December 20
    • David Loeffler (University of Warwick; Simons Professor), Aug 15 - December 15
    • Adam Logan (Carleton University) September 15 - November 30
    • Wieslawa Niziol (École Normale Supérieure de Lyon; Aisenstadt Chair), October 11 - December 12
    • Giovanni Rosso (Concordia University), August 20 - December
    • Ehud de Shalit (University of Jerusalem; Simons Professor), August 23 - October 31
    • Salim Tayou (CICMA postdoc), September 1 - December 20
    • Sarah Zerbes (University College London; Simons Professor), October 15 - December 15