Hamid AHMADINEZHAD  Pliability of Mori fibre spaces in dimension 3 
 I begin with recalling the definition of pliability for Mori fibre spaces, and Fano varieties in particular. Then I explore the strong connection between this invariant and the finite generation of certain Cox rings. This, for instance, highlights the geometry behind the method of maximal singularities, used to prove birational rigidity. Some applications in proving birational rigidity (and hence nonrationality) and birational nonrigidity for some Fano threefolds will be mentioned. 
Serge CANTAT  Examples of (pseudo)automorphisms in dimension 3 
 I shall describe examples of complex projective threefolds with
a nice group of automorphisms or pseudoautomorphisms, the dynamics of which is nontrivial. These examples are due to Keiji Oguiso and his coauthors. 
Pierrette CASSOUNOGUES  Field generators 

Let k be a field. A field generator is a polynomial F∈k[X,Y] satisfying k(F,G)=k(X,Y), for some G∈k(X,Y). If G can be chosen in k[X,Y], we call F a "good field generator",
otherwise F is a "bad field generator". These notions were first studied by Abhyankar, Jan and Russell in the 70s. Until 2005, only two examples of bad field generators were known.
We study the behavior of bad field generators under birational morphisms. This lead to the construction of new bad field generators with arbitrary number of dicriticals. Joint work with Daniel Daigle, U. Ottawa. 
JeanLouis COLLIOTTHÉLÈNE  Unverzweigte Kohomologie 

This talk will be part of the PerlenKolloquium (classical colloquium of the institute).
Die Brauergruppe von Varietäten kann man zu verschieden Zwecken benutzen :
 Zeigen, das eine Varietät nicht rational ist, d. h., ihr Funktionenkörper nicht
rein transzendant ist.
 Wenn der Grundkörper ein Zahlkörper ist, zeigen, daβ
das LokalGlobal Prinzip für rationale Punkte nicht gilt (BrauerManinsche Hindernis).
 Die Picardgruppe, d.h. die Klassengruppe von Divisoren, untersuchen (Tatesche Vermutung).
Unverzweigte Kohomologiegruppen sind Verallgemeinerungen der Brauergruppe.
Ich werde erklären, wie man sie zu ähnlichen Zwecken anwenden kann.

Julie DÉSERTI  On cubic birational maps of 3() 
 I will deal with the irreducible components of the set of birational maps of bidegree (3,3), (3,4) and (3,5). 
Alexander DUNCAN  Equivariant Unirationality 

A variety X is unirational if there exists a dominant rational map from
an affine space V to X. I discuss a generalization of this notion which
I call ``Gunirationality.'' Consider a variety X with an action of a
linear algebraic group G. We say that X is Gunirational if there
exists an equivariant dominant rational map from a linear representation
V of G.
I will discuss how existing unirationality constructions in the
arithmetic case can be used to provide constructions in the equivariant
case. I also discuss how progress in the equivariant setting may yield
results in the arithmetic setting. The main objects of study will be
del Pezzo surfaces. 
Frédéric MANGOLTE  Topology of real algebraic varieties of dimension 3 
 We know since Nash (1952) and Tognoli (1973) that any compact smooth manifold M admits a real algebraic model. Namely, given a manifold M, there exists polynomials with real coefficients whose locus of common real zeroes is diffeomorphic to M.
Bochnak and Kucharz proved later that there exists in fact an infinite number of distincts models for a given M. We try therefore to find "simpler" models than the others in a meaning to be specified. In this talk, I will describe the stateoftheart concerning this research program about "simple" real algebraic models for low dimensional varieties.
The situation for curves and surfaces is quite well understood now, and the surface case is already interesting. For real algebraic threefolds, János Kollár opened in 1999 a direction of research thanks to his solution of Minimal Model Program over the reals. We will discuss several Kollár?s conjectures solved since then. 
Andriy REGETA  Lie subalgebras of vector fields and the Jacobian conjecture 

We study Lie subalgebras L of the vector fields Vecc(2) of the affine 2space 2 of constant divergence, and we classify those L which are isomorphic to the Lie algebra aff_{2} of the group Aff_{2}(K) of affine transformations of 2.
We then show that the following statements are equivalent:
(a) The Jacobian Conjecture holds in dimension 2;
(b) All Lie subalgebras L ⊂ Vecc(2) isomorphic to aff_{2} are conjugate under
Aut(2);
(c) All Lie subalgebras L ⊂ Vecc(2) isomorphic to aff_{2} are algebraic. 
Damiano TESTA  Unirationality of certain del Pezzo surfaces of degree two 
 A consequence of the SegreManin Theorem is that a del Pezzo surface of degree two is unirational over the ground field as soon as it contains a general point. I will report on joint work with C. Salgado and T. VárillyAlvarado where we find precise conditions implying unirationality. In particular, we prove that all del Pezzo surfaces of degree two over finite fields are unirational with at most three possible exceptions. 