This volume is the refereed proceedings of an international conference on "In-
tegral Quadratic Forms and Lattices" that was held at Seoul National University in
Korea from June 15th to 19th, 1998. The conference was the inaugural conference
of SANGSAN Mathematical Science Research Building and was sponsored by the
Global Analysis Research Center and the Department of Mathematics of SNU.
The conference covered recent developments in diverse areas related to the the-
ory of quadratic forms and lattices. The volume contains topics such as representa-
tion theory of integral quadratic forms and hermitian forms, local densities, linear
relations, and congruences of theta series, zeta functions of prehomogeneous vector
spaces, lattices with maximal finite matrix groups, globally irreducible lattices, and
Mordell-Weil lattices, to name a few.
The lectures given at the conference and reproduced here were a mixture of
expository lectures covering recent progress in the field and of presentations of
new research results. This volume therefore intends to serve as an introduction to
the current state of knowledge in the arithmetic theory of quadratic forms and at
the same time to represent some of the active directions of research in this field
with selected new results. The selection of topics puts an emphasis on connections
with neighbouring fields like group theory, arithmetic geometry, analytic number
theory and modular forms. Our hope is that this collection will help to develop
such connections with neighbouring fields and to stimulate further research in the
arithmetic theory of quadratic forms.
This book, we hope, serves well not only as an introductory guide for graduate
students but also as a rich reference for researchers in these areas.
We would like to express our thanks to all the participants and especially to the
invited speakers of the conference for their motivating lectures and excellent articles.
We also thank all the referees for their invaluable time spent for these articles.
Special thanks should be given to GARC and its director, Professor Sang-Moon
Kim, and the Department of Mathematics of SNU for sponsoring the conference.
Finally, we would like thank Mi Yoon and company, the graduate students of SNU
working on number theory, for their sincere assistance during the conference.