Geometry Over Nonclosed Fields

Date & Time


Location


April 17-23, 2016

 
Organizers:
Fedor Bogomolov, Courant Institute of Mathematical Sciences
Brendan Hassett, Brown University
Yuri Tschinkel, Simons Foundation

Related Links:

The focus of this third symposium on Geometry Over Nonclosed Fields was zero-cycles and related Chow-theoretic and birational invariants for higher-dimensional algebraic varieties over various fields. Creative applications of “decomposition of the diagonal”, in combination with deformation theory and unramifed cohomology, have led to new proofs of irrationality for complex varieties. We expect these techniques may shed new light on rational points for varieties over non-closed fields, e.g., del Pezzo surfaces over function fields.

Click here for a PDF of the schedule and participant list, or see the Agenda and Participants sections below.

  • Agenda & Slidesplus--large

    Sunday
    8:00 – 10:00 PM Dinner
    Monday Rationality Problems
    9:30 – 11:00 AM Breakfast
    11:00 AM – 12:00 PM Asher Auel: Stable rationality of quadric bundles
    12:00 – 12:30 PM Break
    12:30 – 1:30 PM Sujatha Ramdorai: Birational geometry and derived birational invariants (Slides PDF)
    1:30 – 2:30 PM Lunch
    2:30 – 4:30 PM Discussion & Recreation
    4:30 – 5:00 PM Afternoon Tea & Discussion
    5:00 – 6:00 PM Ivan Cheltsov: Rationality and non-rationality of singular Fano threefolds
    6:00 – 7:00 PM Konstantin Shramov: Fano threefolds with large automorphism groups
    8:00 – 9:30 PM Dinner at the Wintergarden
    Tuesday Arithmetic Problems
    9:30 – 11:00 AM Breakfast
    11:00 AM – 12:00 PM Antoine Chambert-Loir: Motivic Poisson formula and motivic height zeta functions (Slides PDF)
    12:00 – 12:30 PM Break
    12:30 – 1:30 PM Julia Hartmann: Local-Global Principles for Rational Points on Homogeneous Varieties (Slides PDF)
    1:30 – 2:30 PM Lunch
    2:30 – 4:30 PM Discussion & Recreation
    4:30 – 5:00 PM Afternoon Tea & Discussion
    5:00 – 6:00 PM Bruno Kahn: Torsion index of algebraic surfaces
    6:00 – 7:00 PM Raman Parimala: Unramified cohomology of quadric bundles over surfaces
    8:00 – 9:30 PM Dinner
    Wednesday Automorphisms
    8:00 – 9:30 AM Breakfast
    10:00 AM – 2:00 PM Guided Hike to Partnach Gorge
    2:00 – 3:00 PM Lunch
    3:00 – 5:00 PM Recreation & Discussion
    5:00 – 5:30 PM Tea & Discussion
    5:30 – 6:30 PM Misha Verbitsky: Constructing automorphisms of hyperkahler manifolds (Slides PDF)
    7:00 – 8:00 PM Concert
    8:00 – 9:30 PM Dinner
    Thursday Cohomology
    9:30 – 11:00 AM Breakfast
    11:00 AM – 12:00 PM Jean-Louis Colliot-Thélène: A survey on unramified cohomology (Slides PDF)
    12:00 – 12:30 PM Break
    12:30 – 1:30 PM Philippe Gille: Serre’s conjecture II for groups of type E7 (Slides PDF)
    1:30 – 2:30 PM Lunch
    2:30 – 4:30 PM Discussion & Recreation
    4:30 – 5:00 PM Afternoon Tea & Discussion
    5:00 – 6:00 PM Hélène Esnault: Lefschetz theorems (mostly) over finite fields
    6:00 – 7:00 PM Alena Pirutka: Rationality in families and quadric bundles (Slides PDF)
    8:00 – 9:30 PM Dinner
    Friday Geometry Over the Reals
    9:30 – 11:00 AM Breakfast
    11:00 AM – 12:00 PM Olivier Wittenberg: On the integral Hodge conjecture for real threefolds
    12:00 – 12:30 PM Break
    12:30 – 1:30 PM Olivier Benoist: On Hilbert’s 17th problem in low degree
    1:30 – 2:30 PM Lunch
    2:30 – 4:30 PM Discussion & Recreation
    4:30 – 5:00 PM Afternoon Tea & Discussion
    5:00 – 6:30 PM Discussion
    8:00 – 9:30 PM Dinner at Kaminstüberl
  • Participantsplus--large

    Asher Auel Yale University
    Arnaud Beauville Université de Nice
    Olivier Benoist Université de Strasbourg
    Fedor Bogomolov Courant Institute of Mathematical Sciences
    Antoine Chambert-Loir Université Paris-Sud
    Ivan Cheltsov University of Edinburgh and Moscow Higher School of Economics
    Jean-Louis Colliot-Thélène Université Paris-Sud
    Hélène Esnault Freie Universität Berlin
    Philippe Gille Universite Claude Bernard Lyon 1
    Julia Hartmann University of Pennsylvania
    Brendan Hassett Brown University
    Daniel Huybrechts University of Bonn
    Bruno Kahn Institute de Mathematiques de Jussieu-Paris Rive Gauche
    Moritz Kerz Universität Regensburg
    Andrew Kresch Universität Zürich
    Alena Pirutka Centre de Mathématiques Laurent Schwartz
    Yuri Prokhorov National Research University
    Parimala Raman Emory University
    Sujatha Ramdorai Tata Institute of Fundamental Research
    Konstantin Shramov Moscow Higher School of Economics
    Yuri Tschinkel Simons Foundation
    Tony Varilly-Alvarado Rice University
    Misha Verbitsky Moscow Higher School of Economics
    Olivier Wittenberg École Normale Supérieure

 
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