Prerequisites for the Langlands Program∗
نویسنده
چکیده
For learning about the Langlands program, knowledge of Lie-group structure theory, algebraic number theory, algebraic geometry, modular forms, and infinite-dimensional representation theory is appropriate. This article describes how one can get a glimpse of the program with less background than this.
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Gauge Theory and the Geometric Langlands Program
The Langlands program of number theory, or what we might call Langlands duality, was proposed in more or less its present form by Robert Langlands, in the late 1960s. It is a kind of unified scheme for many results in number theory ranging from quadratic reciprocity, which is hundreds of years old, to modern results such as Andrew Wiles’ proof of Fermat’s last theorem, which involved a sort of ...
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