Alexander Merkurjev

Alexander S. Merkurjev (Russian Александр Сергеевич Меркурьев, Alexander Sergeyevich Mercuriev; born September 25, 1955) is a Russian -born American mathematician who deals with algebra.

Merkurjev her PhD in 1979 under Anatoly Yakovlev at the University of Leningrad. He won the 1982 prize for young mathematicians of the Leningrad Mathematical Society and was a professor at the University of Leningrad. In the 1990s, he went to the USA and became a professor at the University of California, Los Angeles.

Merkurjev deals with algebraic groups, quadratic forms, Galoiskohomologie, algebraic K-theory, theory of algebras. In 1981 he proved a fundamental theorem about the structure of central simple division algebras, shortly thereafter expanded in collaboration with Andrei Suslin. These and other works of Merkurjev and Suslin were important in advance of Vladimir Wojewodskis proof of Milnorvermutung and the Bloch- Kato conjecture ( about the description galoiskohomologische higher Milnor K- groups) and provided the motivation for the introduction of important evidence in Wojewodskis standard varieties. Merkurjevs work in 1982 proved a special case of the Bloch- Kato conjecture and his work with Suslin in the 1980s proved more special cases. For his sentence from 1982 Merkurjev later found also " elementary " proofs without the use of algebraic K- theory.

With J. Buhler and Z. Reichstein, he led a "Essential dimension " called new invariants of algebraic structures.

In 1996, he gave one of the plenary at the European Congress of Mathematicians in Budapest (K- theory and algebraic groups). In 2012 he received the Cole prize in algebra. In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( Milnor K- theory and Galois cohomology ). He is a Fellow of the American Mathematical Society.

Writings

• By Max Albert Knusper, Markus Rost, Jean -Pierre Tignol: The book of involution, American Mathematical Society 1998
• By Skip Garibaldi, Jean -Pierre Serre: Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003
• With Richard Ellman, Nikita Karpenko: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008