 Talk of J. Ducoat:
Let W be a finite Coxeter group. A cohomological invariant of W is a morphism of functors between the first cohomology set functor $H^1(./k_0,W)$ and the Galois cohomology functor $H^i(./k_0,C)$, where $C$ is a finite $\Gamma_{k_0}$module. We will state a general vanishing principle for the cohomological invariants of W over a base field of characteristic zero and then use it to describe all the cohomological invariants in the particular case of the Weyl groups of classical type.
 Talk of Y. Hu:
Let K be a field of one of the following two types: 1. (the arithmetic
case) the function field of an integral algebraic curve a padic number
field; 2. (the local henselian case) the fraction field of a
2dimensional henselian excellent local domain with finite residue field.
In the arithmetic case, ColliotThélène, Parimala and Suresh made two
conjectures on the Hasse principle with respect to discrete valuations of
K for the existence of rational points on homogeneous spaces under
connected linear algebraic groups over K: one for projective homogeneous
spaces and another for torsors under semisimple simply connected groups.
They proved the Hasse principle for quadratic forms of rank at least 3
and for torsors under quasisplit semisimple simply connected groups
without E_8 factors. In this talk, we will discuss the Hasse principle
for quadratic forms in the local henselian case as well as the Hasse
principle for torsors under some non quasisplit semisimple simply
connected groups in both cases.
 Talk of R. Lötscher:
The wellknown fiber dimension theorem in algebraic geometry
says that for every morphism f : X > Y of integral schemes of finite type, the
dimension of each nonempty fiber of f is at least dim X  dim Y.
We will discuss two analogues of this theorem, where schemes are replaced by
categories fibered in groupoids and dimension is replaced by essential or canonical
dimension. These analogues will be applied in particular to derive new relations
between the essential dimension and canonical dimension of group schemes.
 Talk of S. Scully:
An (integral) algebraic variety is called compressible if it admits a degree 0 rational endomorphism. Any variety which has a rational point is compressible, but there are several examples of varieties over nonalgebraically closed fields for which this property fails to hold. For instance, it does not hold for any smooth anisotropic quadric with first Witt index equal to 1 (M. Rost, A. Vishik, N. Karpenko). N. Karpenko and A. Merkurjev showed moreover that these quadrics have a stronger property: socalled strong 2incompressibility. An extension of this result to nonsmooth quadrics was later proved by B. Totaro, including the special case of quadrics which have no smooth points at all. Quadrics of the latter type belong to a larger class of nowhere smooth varieties which we call quasilinear hypersurfaces. I will describe an analogue of the KarpenkoMerkurjev theorem for quasilinear hypersurfaces, and discuss some of its applications.
