Alexander Merkurjev

Alexander Merkurjev
Native name Aleksandr Sergeyevich Merkurjev
Born (1955-09-25) September 25, 1955
Saint Petersburg, USSR
Residence United States
Fields Mathematics
Institutions University of California Los Angeles
Alma mater Leningrad University
Doctoral advisor Anatoli Yakovlev
Doctoral students Vladimir Khalin, MIkhail Gruntovich, Roman Bogomolov, Oleg Izhboldin, Nikita Karpenko
Known for Merkurjev–Suslin theorem, cohomological invariants, canonical dimension, book of involutions, essential dimension
Notable awards Cole Prize in Algebra (2012)
Petersburg Mathematical Society Prize (1982)

Aleksandr Sergeyevich Merkurjev (Russian: Алекса́ндр Сергее́вич Мерку́рьев, born September 25, 1955[1]) 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 1980s 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.[2] 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 (for a prime p) and, in joint work with Karpenko, the essential dimension of finite p-groups.[3][4]

Awards

In 1982 Merkurjev won the Young Mathematician Prize of the Petersburg Mathematical Society for his work on algebraic K-theory.[5] 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".[6] In 1995 he won the Humboldt Prize, an international prize awarded to renowned scholars. Merkurjev gave a plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary in 1996.[7]

In 2012 he won the Cole Prize in Algebra for his work on the essential dimension of groups.[8]

In 2015 a special volume of Documenta Mathematica was published in honor of Merkurjev's sixtieth birthday.[9]

Bibliography

Books

References

  1. ↑ Listed in the Library of Congress Online Catalog
  2. ↑ A. Merkurjev (1981). "On the norm residue symbol of degree 2". Dokl. Akad. Nauk SSSR, 261: 542–547 (English trans. Soviet Math. Dokl. 24 (1982), pp.1546–1551).
  3. ↑ A. Merkurjev (2010). "Essential p-dimension of PGL(p^2)". JAMS, 23. pp. 693–712.
  4. ↑ N. Karpenko, A. Merkurjev (2008). "Essential dimension of finite p-groups". Inventiones Mathematicae, 172, no. 3. pp. 491–508.
  5. ↑ "Young mathematician prize of the Petersburg Mathematical Society".
  6. ↑ "Proceedings of the International Congress of Mathematicians, August 3-11, 1986". International Mathematical Union. Merkurjev's talk: Milnor K-theory and Galois cohomology.
  7. ↑ "Speakers and talks at the 2nd European Congress of Mathematics".
  8. ↑ "2012 Cole Prize in Algebra" (PDF).
  9. ↑ "Extra volume of Documenta Mathematica (2015)" (PDF).
  10. ↑ Springer, T. A. (1999). "Review: The book of involutions, by M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol (with a preface by J. Tits)" (PDF). Bull. Amer. Math. Soc. (N.S.). 36 (3): 383–388. doi:10.1090/S0273-0979-99-00780-6.
  11. ↑ Swallow, John (2005). "Review: Cohomological invariants in Galois cohomology, by Skip Garibaldi, Alexander Merkurjev, and Jean-Pierre Serre" (PDF). Bull. Amer. ath. Soc. (N.S.). 42 (1): 93–98.
  12. ↑ Zaldivar, Felipe (2008). "Review: The Algebraic and Geometric Theory of Quadratic Forms". MAA Reviews.

External links

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