XIth OPORTO MEETING on
GEOMETRY, TOPOLOGY & PHYSICS
From July 12th to July 15th, 2002
COURSES (Detailed)
I. ANDERSON
Group Invariant Solutions and Symmetric Criticality
Ph.A. GRIFFITHS
Abel's Differential Equations
This year marks the bicentennary of the birth of Niels Abel. In hindsight,
one may now see that the general form of Abel's differential equations
for the rational motion of configurations of points on an algebraic curve
was in some ways the decisive event in the development of the theory of
algebraic curves in the nineteenth century. The extension of Abel's differential
equations to configurations of points on higher dimensional algebraic varieties
is one of the central problems in modern algebraic geometry. For my short
course, I propose to give three talks centered around Abel's differential
equations. The first would be a review of the classical version of these
differential equations and of their integration. The second would be an
introduction to the modern form of Abel's differential equations, which
leads even classical analysts into what can only be called post-modern
mathematics. In the third lecture, I would give the general version of
Abel's differential equations and discuss the arithmetic/analytic difficulties
in their integration.
N. KAMRAN
A. VINOGRADOV
A Panorama of Secondary Calculus