Galois cohomology plays a crucial role in various areas of mathematics, particularly in algebraic number theory, algebraic geometry, and group theory. It provides a bridge between the algebraic properties of fields and the geometry of associated algebraic schemes or varieties. For instance, it is an indispensable tool to analyze the existence of rational points on algebraic varieties (e.g. the Brauer-Manin obstruction, the Hasse principle). It lies in the foundations of the modern class field theory (used to study absolute Galois groups). Its non-abelian version is used to study and to classify torsors for algebraic groups (quadratic forms, central simple algebras, Jordan algebras), and the respective projective homogeneous varieties (Severi-Brauer varieties, quadrics).

 

The Massey product is a higher-order cohomology operation defined in algebraic topology by William S. Massey in the 1950s as a generalization of the usual cup product. It has important applications in algebraic topology, particularly in the study of higher homotopy structures. It also provides a tool to capture more intricate algebraic structures and relationships among cohomology classes beyond what the cup product can achieve.

 

It has been discovered recently that the Massey product in Galois cohomology can be effectively applied to study cohomological invariants and torsors of algebraic and finite groups. This workshop will essentially focus on this new emerging approach. It will feature talks on the latest developments in Galois cohomology, cohomological invariants, torsors and applications of Massey products given by senior specialists and young researchers.  A mini-course on Massey products aimed at graduate students attending the workshop is also being planned. .