The benefits of pure mathematics to the society in whole are threefold. The society benefits from the work of applied mathematicians, from interaction of mathematics with other disciplines, and from developing modern curricula to fit the evolution of the modern science and the language of mathematics.
Since its foundation, the Laboratory strives to attract the best scientific minds working in algebraic geometry, in Russia and abroad. The conferences organized by the Laboratory would serve to disseminate the knowledge (both already obtained and newly created); a rich network of international contacts would help to establish its reputation as a major center of science.
Algebraic geometry is one of the most active fields of mathematics. Originally understood as a study of geometric structures by the means of commutative algebra, now algebraic geometry incorporates the methods of complex analysis (via Hermander's L^2-estimates and Ohsawa-Takegoshi extension theorem), PDE and mathematical physics (due to Donaldson's and Yau's fundamental advances on Hermitian-Einstein and Kaehler-Einstein structures), representation theory and differential geometry (Mumford, Bogomolov, Yau).
The importance of algebraic geometry is hard to overestimate. For the last 50 years, almost 1/3 of Fields medals were awarded for the research in algebraic geometry; algebraic geometry is heavily used in string physics, computer algebra systems and cryptography.
The Soviet school of algebraic geometry, founded by Shafarevich, was one of the most influental and illustrous (Manin, Iskovskikh, Tyurin, Bogomolov, Beilinson, Drinfeld). Since 1990-ies it dispersed through the scientific emigration, and the importance of research originating from Russia diminished. To rectify this situation, High School of Economics has hired Fedor Bogomolov to preside over a newly created Laboratory of Algebraic Geometry, an active research and teaching body of yound mathematicians, working in the mathematical department of HSE.
Department of Mathematics of HSE was created on a rich mathematical foundation, provided by the Independent University of Moscow (IUM). This institution was founded in early 1990-ies by such luminaries as V. I. Arnol'd, S. P. Novikov, A. A. Beilinson and V. A. Vassiliev, together with their Western colleagues - R. MacPherson and P. Deligne from Princeton's Institute of Advanced Studies. Since then, Independent University became a very active and successful reseach and teaching body. Jointly with its sister institution, Moscow Center of Continuous Mathematical Education, IUM revolutionized methods of teaching mathematics, and prepared many brilliant scientists, among them the Fields medalist A. Okun'kov.
Now these teaching methods are implemented on a more organized basis in the newly created mathematical faculty of HSE. The hospitable setting provided by HSE turned out to be very conductive to both research and teaching, and Department of Mathematics at HSE is growing fast to become one of the finest institutions in the country.
To coordinate the HSE'e effort of attracting the best scientists (both Russian and foreign), a Laboratory of Algebraic Geometry was created, under the leadership of a distinguished scientist from New-York University, Professor Fedor A. Bogomolov, formerly from Steklov Institute of Mathematics.
The mission of the Laboratory of Algebraic Geometry is fivefold. It is
- To attract best scientists working in algebraic geometry, both in Russia and in the West.
- To serve the wide community in disseminating the knowledge, to organize conferences and workshop, eith support of the parent institutions, Mathematical department of HSE and the Independent University.
- To discover and implement the new curriculum, following the demands of the growing science and technology.
- To nurture the creative side of the high school education, through the mathematical schools, summer camps, olympiads and by supporting the Moscow Center of Continuous Mathematical Education.
And the most important mission is (of course)
- To research, to stay at the bleeding edge of modern science - as every scientist should.
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