US-Sweden Cooperative Research: Hyperbolic Geometry and Quasiconformal Mappings

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This award will support Dr. Ravi Kulkarni, Department of Mathematics, Queens College, City University of New York, to spend nine months at the Mittag-Leffler Institute in Stockholm, Sweden. This institute, which has a century-old tradition in classical analysis, is sponsoring a special academic year on the topic of "Hyberbolic Geometry and Quasiconformal Mappings." During this year, Dr. Kulkarni will carry out collaborative research with two Finnish mathematicians, Drs. Seppo Rickman and Pekka Tukia, University of Helsinki, who will be directing this special program at the institute. Dr. Rickman has carried out a pioneering work in quasiconformal and more generally quasiregular mappings. Through this work it has become increasingly evident that this "quasiregular" direction is a right generalization of the classical geometric function theory. Notably Rickman obtained complete generalizations of the classical Picard's theorem in higher dimensions. Recently he has also obtained strong forms of the Nevanlinna-Ahlfors defect relations in higher dimensions. Dr. Tukia also has a worldwide reputation due to his extensive work on the extension properties of quasiconformal mappings and geometric features of the classical theories of fuchsian and kleinian groups. During his stay at the institute, Dr. Kulkarni will focus on the following: (1) the structure of moduli spaces of Riemann surfaces (2) the study of topological aspects of fuchsian and kleinian groups and their generalizations (3) mobius structures. The results of this research should make a significant contribution to understanding this area of geometric analysis.