Jean-Louis Colliot-Thélène

"Résolutions flasques des groupes réductifs connexes".

Alexander Merkurjev

"Algebraic cobordism theory".

I plan to talk about the Algebraic Cobordism Theory introduced by F.Morel and M.Levine.

1. Oriented Borel-Moore functors.
2. Definition of algebraic cobordism.
3. Localization, homotopy invariance, projective bundle formula.
4. The cobordism ring of a point. Lazard ring.
5. Generalized degree formula.
6. Algebraic cobordism and algebraic K-theory.
7. Algebraic cobordism and Chow groups.

Raman Parimala

"Period-index problem for central simple algebras over function fields of surfaces, d'après de Jong."

In these lectures we shall discuss the proof of Let k be an algebraically closed field and K a function field in two variables over k. Then for every central simple algebra A over K whose exponent is coprime to the characteristic of k, the index of A coincides with the exponent of A.

Albrecht Pfister

"Personal perspectives of ..."

Alexander Sivatski

"Applications of Clifford Algebra to involutions and quadratic forms".

Andrei Suslin

"An introductory course of motivic cohomology"

1) Nisnevich Sheaves with transfers and their main properties, complexes Z(n) and motivic cohomology.
2) Motivic cohomology and Milnor K-theory
3) Voevodsky Cancellation Theorem, Cohomology Purity and Cohomology with supports.
4) Rational contractibility of the complex Z(n) and reduction of the Beilinson-Lichtenbaum Conjecture to the Bloch-Kato Conjecture.
5) Steenrod and Milnor operations in Motivic Cohomology, Margolis acyclicity.
6) Motivic cohomology of Pfister quadrics and a sketch of the proof of the Milnor Conjecture.

Alexander Zainoullin

"On motivic decomposition for relative cellular spaces".