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In his 1974 seminal paper 'Elliptic modules', V G Drinfeld
introduced objects into the arithmetic geometry of global function
fields which are nowadays known as 'Drinfeld Modules'. They have
many beautiful analogies with elliptic curves and abelian
varieties. They study of their moduli spaces leads amongst others
to explicit class field theory, Jacquet-Langlands theory, and a
proof of the Shimura-Taniyama-Weil conjecture for global function
fields.This book constitutes a carefully written instructional
course of 12 lectures on these subjects, including many recent
novel insights and examples. The instructional part is complemented
by research papers centering around class field theory, modular
forms and Heegner points in the theory of global function
fields.The book will be indispensable for everyone who wants a
clear view of Drinfeld's original work, and wants to be informed
about the present state of research in the theory of arithmetic
geometry over function fields.
This volume is the record of a workshop on differential equations
and the Stokes phenomenon, held in May 2001 at the University of
Groningen. It contains expanded versions of most of the lectures
given at the workshop. To a large extent, both the workshop and the
book may he regarded as a sequel to a conference held in Groningen
in 1995 which resulted in the book The Stokes Phenomenon and
Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der
Put, editors), also published by World Scientific (1996).
Both books offer a snapshot concerning the state of the art in
the areas of differential, difference and q-difference equations.
Apart from the asymptotics of solutions, Painleve properties and
the algebraic theory, new topics addressed in the second book
include arithmetic theory of linear equations, and Galois theory
and Lie symmetries of nonlinear differential equations.
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