Advanced School and Workshops on Discrete Groups in Complex Geometry

University Of Maryland, College Park, College Park MD

Investigators

Abstract

The study of discrete groups in complex geometry originates in the pioneering work of H. Poincare in the early 20th Century, studying solutions of certain differential equations on the complex line. This led to the concept of Fuchsian and Kleinian groups: these are discrete groups of automorphisms of the Riemann sphere. This turns out to be closely related to hyperbolic geometry, where Fuchsian and Kleinian groups are groups of isometries of hyperbolic two and three dimensional spaces. The study of these types of discrete group-actions on complex spaces, and their generalizations to higher dimensions and to other geometries, has played for decades a major role in complex geometry and in holomorphic dynamics. This will be the first conference to bring together workers in the fields of holomorphic dynamics, higher dimensional complex Kleinian groups, and the deformation theory of geometric structures on manifolds. The aim of this School and Workshop is to introduce young mathematicians to the foundations of the field, some of its major developments and tools used for its study. The meeting will start with elementary courses to provide the foundations of the theory. Then advanced courses and a workshop will lead the participants to some of the important areas of current research in complex geometry. At the end of the workshop a problem session will address the future directions of these fields. This meeting will bring together researchers in diverse, but related areas, from all over the world. Graduate students and postdocs especially will benefit from the minicourses being offered in the summer school. Priority will be given to graduate students, young researchers, under-represented groups and mathematicians with no other available funding. Researchers working in the third world countries involved in ICTP and Europe will have a chance to interact with their counterparts from America.