event
Lundi 13 juin 2022
place
IRMA Strasbourg

The aim of the summer school is to provide an introduction to recent advances in the understanding of the number-theoretic content of the cohomology of arithmetic groups and of algebraic K-groups of number rings. Uncovering this information reveals deep connections with algebraic geometry, namely with the theory of motives and with motivic homotopy theory. Surprisingly, this happens even when the arithmetic groups under consideration are not directly linked with algebraic varieties.

Organizers Jitendra Bajpai (MPIM Bonn) Mattia Cavicchi (IRMA Strasbourg)

Scientific committee Frédéric Déglise (ENS Lyon) Günter Harder (MPIM Bonn) Wiesława Nizioł (IMJ-PRG)

The mini-courses will cover the following topics:

  • Neil Dummigan - "Approaches to Harder's conjecture on Eisenstein congruences"
  • Clément Dupont - "Mixed Tate motives, Dedekind zeta values, and polylogarithms"
  • Sophie Morel - "Weighted cohomology of Shimura varieties"
  • Paul Arne Østvær - "Motives and Hermitian K-theory of number rings"
  • Kartik Prasanna - "Motivic cohomology and cohomology of arithmetic groups"

The summer school will also feature talks from young researchers.

Registrations : see the official web site.

  • Lundi 13 juin 2022

  • 09:00

    Mixed Tate motives, Dedekind zeta values, and polylogarithms I - Dedekind zeta values, polylogarithms, and Zagier’s conjecture

    — Clément Dupont

  • 10:30

    Weighted cohomology of Shimura varieties I

    — Sophie Morel

  • 11:30

    Motives and Hermitian K-theory of number rings I

    — Paul Arne Østvær

  • 15:00

    Approaches to Harder's conjecture on Eisenstein congruences I

    — Neil Dummigan

  • 16:30

    Motivic cohomology and the cohomology of arithmetic groups I

    — Kartik Prasanna

  • 17:30

    On the non-vanishing of certain p-adic regulators

    — Alexandre Maksoud

  • 17:50

    p-adic variation of the Asai–Flach Euler system

    — Arshay Sheth

  • Mardi 14 juin 2022

  • 09:00

    Motives and Hermitian K-theory of number rings II

    — Paul Arne Østvær

  • 10:30

    Motivic cohomology and the cohomology of arithmetic groups II

    — Kartik Prasanna

  • 11:30

    Mixed Tate motives, Dedekind zeta values, and polylogarithms II - Cohomology and (mixed Tate) motives

    — Clément Dupont

  • 15:00

    Weighted cohomology of Shimura varieties II

    — Sophie Morel

  • 16:30

    Approaches to Harder's conjecture on Eisenstein congruences II

    — Neil Dummigan

  • 17:30

    On the motivic cohomology of the Nisnevich classifying space of PGL_n

    — Fabio Tanania

  • 17:50

    Recent computations in function fields t-motivic cohomology

    — Quentin Gazda

  • 18:10

    Isoshtukas over Z

    — Sergey Yakovenko

  • Mercredi 15 juin 2022

  • 09:00

    Motivic cohomology and the cohomology of arithmetic groups III

    — Kartik Prasanna

  • 10:30

    Weighted cohomology of Shimura varieties III

    — Sophie Morel

  • 11:30

    Approaches to Harder's conjecture on Eisenstein congruences III

    — Neil Dummigan

  • Jeudi 16 juin 2022

  • 09:00

    Approaches to Harder's conjecture on Eisenstein congruences IV

    — Neil Dummigan

  • 10:30

    Motives and Hermitian K-theory of number rings III

    — Paul Arne Østvær

  • 11:30

    Motivic cohomology and the cohomology of arithmetic groups IV

    — Kartik Prasanna

  • 15:00

    Mixed Tate motives, Dedekind zeta values, and polylogarithms III - The Tannakian formalism and motivic complexes

    — Clément Dupont

  • 16:30

    Functional equations for Nielsen polylogarithms

    — Steven Charlton

  • 16:50

    Relations among block graded multiple zeta values

    — Adam Keilthy

  • 17:10

    Mahler measures and exactness: a periodic stroll

    — Riccardo Pengo

  • 17:30

    Logarithmic vector-valued automorphic forms: growth and lifting

    — Subham Bhakta

  • 17:50

    Theta lifts and cycle integrals

    — Ingmar Metzler

  • 18:10

    Cohomology of Hermitian modular varieties and the unitary Kudla conjecture

    — Jiacheng Xia

  • Vendredi 17 juin 2022

  • 09:00

    Weighted cohomology of Shimura varieties IV

    — Sophie Morel

  • 10:30

    Mixed Tate motives, Dedekind zeta values, and polylogarithms IV - Recent progress

    — Clément Dupont

  • 11:30

    Motives and Hermitian K-theory of number rings IV

    — Paul Arne Østvær

  • 16:00

    IRMA Colloquium - Branching laws for representations and for cohomology

    — Dipendra Prasad