一小时邀请报告简介之十七：数学的美与用途

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一小时邀请报告简介之十七：数学的美与用途
（转自2006年国际数学家大会官方网站）

Plenary Lecture: Michèle Vergne
Mathematical Beauty and Usefulness

One of the main characteristics of mathematics is that it tends to look for theories that generalize the results. It is not enough to solve a particular problem, but rather all problems of the same type. Dimensions 2 or 3, which are easy to imagine, to see and to feel, do not suffice in mathematics. Results for dimension “n” are sought, where “n” can be any number. A similar case could be that concerning group action. It is easy for everyone to imagine a symmetry; taking the case a little further we can speak of a “symmetry group”, such as that describing all the symmetries of all the objects, and generalizing this idea we arrive at the “group actions”. These are groups in which all the elements act as a “bijective map” in some set. These groups of “non-visible symmetries” are the object of study in “Equivariant Cohomology”, which is a theory of algebraic topology applied to a space with group action. At the coming ICM2006 International Congress of Mathematicians in Madrid,  Michèle Vergne will deliver a lecture on this branch of mathematics, which to the uninitiated must seem to be the most abstract subject imaginable.

Despite appearing to be exceedingly remote from daily life, Vergne is at pains to point out that the subject has very practical uses. “The aim of my lecture is to demonstrate how theorems of localization in equivariant cohomology not only yield mathematical formulae of great beauty, they also stimulate progress in algorithmic computation”.

Michèle Vergne was born in 1943 in L’Isle Adam, Val d’Oise (Francia). She graduated from the École Normale Supérieure de Jeunes Filles in 1966, and obtained her PhD at the University of Paris in 1971. After working for several years at the MIT (Massachusetts Institute of Technology), she returned to her native France, where she is currently head of research at the CNRS “Classe exceptionelle”. In 1997, she was awarded the Ampère Prize by the French Academy of Sciences, of which she has been a member since 1998. She has also been a member of the American Academy of Arts and Sciences since 1998.

Speaker: Michèle Vergne
Title: Applications of Equivariant Cohomology
Date: Saturday, 26 August: 11:45-12.45