Alexander Merkurjev
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Alexander Merkurjev | |
|---|---|
| Born | September 25, 1955 |
| Alma mater | Leningrad University |
| Known for | Merkurjev-Suslin theorem, book of involutions, essential dimension |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of California Los Angeles |
| Doctoral advisor | Anatoli Jakovlev |
| Doctoral students | Nikita Karpenko |
Alexander Merkurjev (Template:Lang-ru) is a Russian-born American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles.
Work
Merkurjev's work focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K-theory and central simple algebras. In the early 1980's Merkurjev 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[1]. In subsequent work with Suslin this was extended to higher torsion. More recently these results were generalized in the norm residue isomorphism theorem (previously known as Bloch-Kato conjecture), proven in full generality by Rost and Voevodsky.
In the late 1990's 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 (for a prime p)[2] and, in joint work with Karpenko, the essential dimension of finite p-groups.[3].
Awards and Distinctions
In 1982 Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory. [4] Later in 1995 he won the Humboldt Prize. Merkurjev gave a plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary, 1996.[5]
References
- ^ A. Merkurjev (1981). "On the norm residue symbol of degree 2". Dokl. Akad. Nauk SSSR, 261. pp. 542–547
(English trans. Soviet Math. Dokl. 24 (1982), pp.1546–1551).
{{cite web}}: Italic or bold markup not allowed in:|publisher=(help); Missing or empty|url=(help); line feed character in|pages=at position 8 (help) - ^ A. Merkurjev (2010). "Essential p-dimension of PGL(p^2)". JAMS, 23. pp. 693–712.
- ^ N. Karpenko, A. Merkurjev (2008). "Essential dimension of finite p-groups". Inventiones Mathematicae, 172, no. 3. pp. 491--508.
- ^ "Young mathematician prize of the [[Petersburg Mathematical Society]]".
{{cite web}}: URL–wikilink conflict (help) - ^ "Speakers and talks at the 2nd European Congress of Mathematics".
Bibliography
- with Max-Albert Knus, Markus Rost, Jean-Pierre Tignol: The book of involutions, American Mathematical Society 1998.
- with Skip Garibaldi, Jean-Pierre Serre: Cohomological Invariants in Galois Cohomology, American Mathematical Society 2003.
- with Richard Elman, Nikita Karpenko: Algebraic and geometric theory of quadratic forms, American Mathematical Society 2008.