Quote:Each summer since 1996,algebraic geometers and algebraists in Norway have organised a summer school in Nordfjordeid, a small place in the western part of Norway. In addition to the beauty of the place, located between the mountains, close to the fjord and not far from the Norway's largest glacier, a reason for going there is that Sophus Lie was born and spent his few first years in Nordfjordeid, so it has a flavour of both the exotic and pilgrimage. It is also convenient: the municipality of Eid has created a conference centre named after Sophus Lie, aimed at attracting activities to fillthe summer term of the local boarding school.
The summer schools are a joint effort of the four universities in Norway - the universities of Tromse, Trondheim, Bergen and Oslo. They are pri- marily meant as training for Norwegiangraduate students, but have over the years attracted increasing numbers ofstudents from other parts of the world, adding the value of being international to the schools.
The themes of the schools have been varied, but build around some cen- tral topics in contemporary mathematics. The format of the school has by now become tradition - three international experts giving independent, but certainly connected, series of talks with exercise sessions in the evening, over five or six days.
In 2001 the organising committee consisted of Stein Arild Stromme from the University of Bergen, Loren Olson from the University of Tromse, and Kristian Ranestad and Geir Ellingsrud from the University of Oslo. We wanted to make a summer school giving the students insight in some of the new interactions between differential and algebraic geometry. The three topics wefinally chose, Riemannian holonomy and calibrated geometry, Calabi-Yau manifolds and mirror symmetry, and Compact hyperkiihler manifolds, are parts of the fascinating current development of mathematics, and we think they illustrate well the modern interplay between differential and algebraic geometry.
Wewerefortunate enough to get positive answers when weasked Dominic Joyce, Mark Gross and Daniel Huybrechts to give the courses, and we are thankful for the great job the three lecturers did, both on stage in Nord- fjordeid and by writing up the nice notes which have now developed into this book.
Geir Ellingsrud