Geometry Over Nonclosed Fields

April 17-23, 2016

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

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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 & Slides

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

Participants

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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