AWS 2005: Home Page of Matsumoto's Lecture |
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A concrete introductory article is a paper by Y. Ihara at ICM 90: "Braids, Galois Groups, and Some Arithmetic Functions", Proceedings of ICM 90, PP.99-120. This paper is compactly written and contains still-open problems, but at many places it seems too compact. There are stated many facts with "it is easy to see", but at least for me, most of them are not easy. Motivated students may read this paper, and try the references there.
My present plan is to lecture on the basic facts on algebraic fundamental groups, and then on problems arising from its Lie algebraization, such as those explained in Section 5 of Ihara's ICM 90 paper.
I would like to assume that the audiences have some knowledge on usual topology, namely, classical fundamental groups, unramified coverings, and universal coverings. I would like to assume some basic knowledge on Galois theory of field extension. It is desirable to know the definition of projective limits, profinite completion of groups: for example, I recommend to read PP.116-121 of "Algebraic Number Theory," J.W.S. Cassels and A. Frohlich Ed., Academic Press 1967. I shall use the basic terminologies from category theory. Please learn the definition of categories, functors and the natural transformation (=morphisms between functors). The following technical terms are related to my lecture. My assumption is that most of students know only little about the following terminology, but it would be good to list them here: students may learn some of them in advance, for example by looking at dictionaries like Encyclopedic dictionary of mathematics. Vol. I-IV, MIT Press, Cambridge, MA, 1987.
(To say the truth, I myself am very scared to give a lecture course in such an international school, in English!)
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