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CRM - University of Ottawa Distinguished Lecture Series

MODIFICATION:Title and Abstract added
TITLE:Cohomological invariants of algebraic groups
SPEAKER:Alexander Merkurjev (UCLA)
DATE:Vendredi, 30 Aoùt 2013
TIME:3:30 pm
ROOM:B005
ABSTRACT:

The notion of a cohomological invariant of an algebraic group was introduced by J.P. Serre. A survey of old a new results will be given in the talk.

About the speaker: The work of Merkurjev focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980s he proved a fundamental result about the structure of central simple algebras of period dividing 2, which relates the 2-torsion of the Brauer group with Milnor K-theory. In subsequent work with Suslin this was extended to higher torsion as the Merkurjev–Suslin theorem, recently generalized in the norm residue isomorphism theorem (previously known as the Bloch-Kato conjecture), proven in full generality by Rost and Voevodsky. In the late 1990s Merkurjev gave the most general approach to the notion of essential dimension, introduced by Buhler and Reichstein, and made fundamental contributions to that field. In particular Merkurjev determined the essential p-dimension of central simple algebras of degree p^2 (for a prime p) and, in joint work with Karpenko, the essential dimension of finite p-groups.

In 1982 Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory. In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley, California, and his talk was entitled "Milnor K-theory and Galois cohomology". In 1995 he won the Humboldt Prize, an international prize awarded to renowned scholars. In 1994 Merkurjev gave a plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary. In 2012 he won the Cole Prize in Algebra for his work on the essential dimension of groups.