7  11 January 2019, in Charmey
(near Gruyères, Fribourg, Switzerland)
Olivier Benoist (ENS Paris)

Algebraic cycles on real algebraic varieties 
Dan Loughran (University of Manchester)  Rational points on varieties 
Etienne Mann (University of Angers)

Algebraic stacks 
Monday January 9 
Tuesday January 10 
Wednesday January 11 
Thursday January 12 
Friday January 13 
12h30 welcome 
breakfast 8h459h45 minicourse 1 10h1511h15 minicourse 2 11h4512h45 minicourse 3 
breakfast 8h459h45 minicourse 1 10h1511h15 minicourse 2 11h4512h45 minicourse 3 
breakfast 8h459h45 minicourse 1 10h1511h15 minicourse 2 11h4512h45 minicourse 3 
breakfast 8h459h45 minicourse 1 10h11h minicourse 2 11h1512h15 minicourse 3 
lunch  lunch  lunch  lunch  
14h3015h30 minicourse 1 16h0017h00 minicourse 2 17h3018h30 minicourse 3 dinner 
time for discussion / enjoying the mountain side 17h2018h10 tba 18h3019h20 tba dinner 
time for discussion / enjoying the mountain side 17h2018h10 tba 18h3019h20 tba dinner 
time for discussion / enjoying the mountain side 17h2018h10 tba 18h3019h20 tba dinner 
VIVA GRUYERE Charmey, Rte des Arses 4, 1637 Charmey
The journey to Charmey is 2h10 from Geneva, 2h30 from Basel/Zürich, 1h30 from Lausanne.
See timetables on www.cff.ch, the bus stop is "Charmey (Gruyère), Le Chêne". The place is very close to the bus stop.
 
The real locus of a smooth projective real algebraic variety is a differentiable manifold. How much of its topology can be seen by algebraic geometers? For instance, are all differentiable submanifolds close to the real locus of an algebraic subvariety? Homologous to the real locus of an algebraic subvariety? We will explain classical results, progress in collaboration with Olivier Wittenberg, and open questions.
 
 
The topic of rational points on varieties is a venerable one, and is the modern way to study solutions to Diophantine equations. The fundamental problems are to determine whether a given variety has a rational point, and if so, "how many" rational points it has. We shall begin with the study of rational points on simple classes of varieties over the field of rational numbers, and introduce tools such as heights, localglobal principles, and techniques from analytic number theory. With these tools in hand, towards the end of the course we shall study the problem of existence of rational points in families of varieties.
 
 
In these lectures, we will first explain the motivation of stacks, then explain the notion fibered categories in groupoids. After, we will give the definition of stacks and algebraic stacks. We will give a lot of easy examples where we can compute everything. At the end, we will define the orbifold cohomology and may be we will explain the root construction and how to define a toric stack. 
 
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Olivier Benoist (Paris)
Fabrizio Barroero (Basel)
Cinzia Bisi (Ferrara)
Anna Bot (ETH)
Jérémy Blanc (Basel)
Alberto Calabri (Ferrara)
Jung Kyu Canci (Basel)
Benoît Dejoncheere (Lyon)
Gabriel Dill (Basel)
Adrien Dubouloz (Dijon)
Sara Durighetto (Ferrara)
Andrea Fanelli (Versailles)
Linda Frey (Copenhagen)
Pascal Fong (Basel)
Richard Griffon (Basel)
Philipp Habegger (Basel)
Isac Hedén (Warwick)
Lucy JauslinMoser (Dijon)
Stéphane Lamy (Toulouse)
Pierre Le Boudec (Basel)
Anne Lonjou (Basel)
Dan Loughran (Manchester)
Frédéric Mangolte (Angers)
Etienne Mann (Angers)
Giao Nguyen (Ferrara)
Erik Paemurru (Loughorough)
Joachim Petit (Basel)
Quentin Posva (EPFL)
Julia Schneider (Basel)
Ursina Schweizer (EPFS)
Samuel Streeter (Manchester)
Axel Supersac (Angers)
Ronan Terpereau (Dijon)
Ettore Turatti (Dijon)
Christian Urech (Imperial College)
Immanuel van Santen (Basel)
Francesco Veneziano (Pisa)
Egor Yasinsky (Basel)
Sokratis Zikas (Basel)
Susanna Zimmermann (Angers)
To register write an email to Susanna Zimmermann until the beginning of November.
Philipp Habegger (University of Basel)
Ronan Terpereau (University of Burgundy)
Susanna Zimmermann (University of Angers)
Here are the previous ones:
1st, 2nd , 3rd, 4th, 5th, 6th, 7th swissfrench workshop in Algebraic Geometry
We gratefully acknowledge support from:
ANR FIBALGA
Institut de Mathématiques de Bourgogne
GDR Singularités (CNRS)
ISITEBFC Project Motivic Invariants of Algebraic Varieties
LAREMA
PEPS (CNRS)
Swiss Academy of Sciences
Swiss doctoral program (cuso)
Swiss mathematical society
University of Angers
University of Basel
University of Rennes (CNRS)