一小时邀请报告简介之十一：黎曼曲面上的网球

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一小时邀请报告简介之十一：黎曼曲面上的网球
（转自2006年国际数学家大会官方网站）

Plenary Session: Ib Madsen
The Surfaces of a Brave New World

In “Brave New World”, Aldous Huxley wrote about “Riemann Surface Tennis”, a game popular with the upper classes. However, in the Spanish version of the novel, the translator gave it the name of ‘Riemann tennis’, which detracted somewhat from Huxley’s incidental attempt to popularize mathematics. This sport was practised on a Riemann surface, which means that once the edges of the court have been identified, if the ball exceeds them and goes out, rather than lose a point, the player must be ready to receive a duplicate of the same ball from another part of the surface. Ib Madsen will talk about these curious surfaces in one of the plenary lectures to be given at the next International Congress of Mathematicians in Madrid.

The lecture by this Danish mathematician revolves around how these surfaces are addressed from the point of view of topology, a subject a great importance for many areas of mathematics and theoretical physics. In fact, these surfaces have given rise to one of the most imaginative proposals to have emerged cosmology in recent years: wormholes. This a black hole, which swallows up everything that comes its way, connected to a white hole, which repels or rejects matter at an unpredictable point in the universe, distant from the first.

Madsen states that there are four keys to his lecture: the relation with Mumford’s Standard Conjecture on cohomology in the studied space with a large number of “holes” in the space; the versions for large dimensions belonging to the category of Riemann surfaces (the possible value for quantum gravity); the topological versions of Gromov–Witten moduli spaces, and the stable homology of the automorphism groups of free groups.

Ib Madsen was born in Copenhagen in 1942. In 1970 he obtained his doctorate in mathematics from the University of Chicago. Since 1971, he has worked at the University of Aarhus (Denmark), where in 1983 he obtained a full professorship. He is a member of the Danish, Swedish and Norwegian Royal Academies of Sciences. He has received much recognition throughout his career, and in 1978 he attended the International Congress of Mathematicians as an invited speaker in one of the areas.

Speaker: Ib Madsen
Title: Moduli Spaces From a Topological Viewpoint
Date: Friday, August 25th: 09:00-10:00

ICM2006 Scientific Programme: http://www.icm2006.org/scientificprogram/plenarylectures/
（转自2006年国际数学家大会官方网站）

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