Geometry Over Nonclosed Fields (2016)
Organizers:
Fedor Bogomolov, Courant Institute of Mathematical Sciences
Brendan Hassett, Brown University
Yuri Tschinkel, Simons Foundation
Related Links:
- 2012 Simons Symposium on Geometry Over Nonclosed Fields
- 2015 Simons Symposium on Geometry Over Nonclosed Fields
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.
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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 -
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