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Vladimir Gershonovich Drinfeld

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1954

Kharkov, Ukraine

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Vladimir Drinfeld studied at Moscow University from 1969 until 1974. He graduated in 1974 and remained at Moscow University to undertake research under Yuri Ivanovich Manin's supervision. Drinfeld completed his postgraduate studies in 1977 and he defended his "candidate" thesis in 1978 at Moscow University. The "candidate" thesis is the Russian equivalent of the British or American Ph.D.

Since 1981 Drinfeld has been working at B Verkin Institute for Low Temperature Physics and Engineering of the Academy of Sciences of the Ukraine. Drinfeld defended his "doctor" thesis in 1988 at Steklov Institute, Moscow. The "doctor" thesis is the Russian equivalent of German habilitation .

On 21 August 1990 Drinfeld was awarded a Fields Medal at the International Congress of Mathematicians in Kyoto, Japan:

... for his work on quantum groups and for his work in number theory .

A Jaffe and B Mazur, write in about Drinfeld's work which led to the award of the Fields Medal:

Drinfeld's interests can only be described as "broad". Not only do they span work in algebraic geometry and number theory, but his most recent ideas have taken a strikingly different direction: he has been doing significant work on mathematical questions motivated by physics, including the relatively new theory of quantum groups.

Drinfeld defies any easy classification ... His breakthroughs have the magic that one would expect of a revolutionary mathematical discovery: they have seemingly inexhaustible consequences. On the other hand, they seem deeply personal pieces of mathematics: "only Drinfeld could have thought of them!" But contradictorily they seem transparently natural; once understood, "everyone should have thought of them!"

Drinfeld's main achievements are his proof of the Langlands conjecture for GL(2) over a functional field; and his work in quantum group theory. Although he only proved a special case of the Langlands conjecture, Drinfeld has introduced important new ideas in his solution and made a real breakthrough. He introduced the idea of an elliptic module in his proof and this notion is leading to a whole new topic within number theory.

The interactions between mathematics and mathematical physics studied by Atiyah led to the introduction of instantons - solutions, that is, of a certain nonlinear system of partial differential equations , the self-dual Yang-Mills equations, which were originally introduced by physicists in the context of quantum field theory. Drinfeld and Manin worked on the construction of instantons using ideas from algebraic geometry.

In 1992 Drinfeld was elected a member of the Academy of Sciences of the Ukraine.

Source:School of Mathematics and Statistics University of St Andrews, Scotland