ON THE OCCASION OF HIS 60TH BIRTHDAY

## June 23-24, 2005 | ## St Petersburg, RUSSIA |

Sergei Vladimirovich Vostokov was born on April 13, 1945. Since 1963 he has been working in St. Petersburg University.

His most famous mathematical papers deal with central topics of local number theory. He has studied explicit formulas for the Hilbert symbol in local and multidimensional local fields, and for the generalized Hilbert symbol associated to various classes of formal groups. He published also a number of papers on Galois module structure of local fields and other topics.

As early as in 1978 using some of the previous works of Shafarevich and Hasse, S.V.Vostokov established his ground formula for the Hilbert symbol. His formula provides a simple and efficient way to calculate values of the symbol. It is the most universal formula for the Hilbert symbol (there are more than ten other formulas). In addition, since the formula is given for all values of the arguments, one has a new symbol-pairing of the multiplicatie group. This pairing plays a fundamental role in number theory and arithmetic geometry. The symbol is often called Vostokov's symbol. It is a wild (and therefore difficult) generalization of the tame symbol. The definition of Vostokov's symbol is independent of class field theory, and this enables one to use its generalizations in proofs of deep results in arithmetic geometry. Explicit formulas for the Hilbert symbol have played an important role in several advances in arithmetic geometry in last 25 years: we can mention works of Coates-Wiles, Wiles, Kato.

S.V.Vostokov created a new direction in number theory in St. Petersburg; it can be called "Constructive approach in number theory". He organized numerous international conferences in the Euler institute.