All talks, except the last talk on Monday, will take place in the Petit Amphi
of the Département de Mathématiques d'Orsay (access).
The Poster Session will take place in the Salle du thé.
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 

09:00  09:30  Welcome and registration  
09:30  10:50  Klingler  Brotbek  VárillyAlvarado  Favre  Favre 
11:10  12:30  VárillyAlvarado  Klingler  Brunebarbe  Klingler  Brotbek 
Lunch break  Lunch break  Lunch  Lunch break  Lunch  
14:00  15:20  Brotbek  SAGA**  Brunebarbe  
15:40  17:00  Brunebarbe*  VárillyAlvarado  Favre  
17:00  19:00  Poster Session*** 
**The Tuesday 30 session of the regular seminar Séminaire Arithmétique et Géométrie Algébrique (SAGA), by Bruno Klingler, will take place in Salle 117119.
***The Poster Session will take place in the Salle du thé.
Lecture series
 Damian BROTBEK:
Jet differentials and hyperbolicity of general hypersurfaces.
A smooth projective complex variety X is said to be hyperbolic if it does not contain any entire curve
(a non constant holomorphic map f : ℂ → X).
The hyperbolicity properties of X are closely related (at least conjecturally) to the positivity properties
of the canonical bundle of X.
For instance, the GreenGriffithsLang conjecture predicts that if X is of general type,
then there exists a proper algebraic subset Z ⊂ X containing all entire curves of X.
In a related direction, in 1970, Kobayashi conjectured that a general hypersurface
H ⊂ ℙ^{n} of sufficiently large degree is hyperbolic.
This conjecture has attracted a lot of attention over the last decades and has only been proved recently by Siu.
The goal of this mini course is to give an introduction to the notion of hyperbolicity and to present another proof of this conjecture of Kobayashi. Along the way we will present the theory of jet differentials, developed among others by Green and Griffiths, Siu, and Demailly, which provides a fruitful way to study the behavior of entire curves. The two other main ingredients of this proof are a suitable Wronskain construction, and the reduction of the problem to the study of a universal family of zero dimensional complete intersections.
 Yohan BRUNEBARBE: Hyperbolicity of moduli spaces of abelian varieties. It is wellknown that the levelN modular curve X(N) has genus at least 2 exactly when N>6. In particular, it follows that there is no nontrivial family of elliptic curves over the complex affine line. In my talks, I will explain how one can use Hodge theory to prove some generalizations of these hyperbolicity statements for moduli spaces of abelian varieties of dimension g>1.
 Charles FAVRE: Degeneration of endomorphisms of projective spaces. We shall describe how one can control the dynamics of a meromorphic family of endomorphisms of the projective space parameterized by the punctured unit disk as one approaches the puncture. Such a control is crucial for instance in the description of special curves in the parameter space of onedimensional rational maps that contain infinitely many postcritically finite maps.
 Bruno KLINGLER:
Bialgebraic geometry.
When X is a complex gdimensional abelian variety,
its universal cover $\stackrel{~}{X}=$
ℂ^{g} is an algebraic variety and many
geometric and arithmetic properties of X can be understood by studying
the transcendance properties of the uniformization map
p: ℂ^{g} → X.
In these lectures we will try to show how a general version of this picture leads to interesting new results and conjectures related to Hodge theory.
 Anthony VÁRILLYALVARADO: Level structures on K3 surfaces and abelian varieties. We will describe boundedness statements for certain level structures over number fields on abelian varieties and K3 surfaces that follow from a combination of recent hyperbolicity results and quantitative arithmetic conjectures. We will also describe unconditional results in the direction of these boundedness statements.