Beckman Fellow 2007-08

Christopher Jay Leininger



Two fundamental objects of study in the field of low-dimensional geometry and topology are (a) mapping class groups of surfaces and Teichmüller theory and (b) Kleinian groups and hyperbolic geometry. As understanding of these two subjects has developed, unexpected analogies have been observed between them, producing some very surprising results.

During his Center appointment, Professor Leininger will participate in a semester-long program, “Teichmüller Theory and Kleinian Groups” at the Mathematical Sciences Research Institute in Berkeley, California. The purpose of the program is to bring together experts in the two fields and further explore the connections between them.

Professor Leininger expects the program to enrich his current project to investigate the analogy between two fundamental objects in low-dimensional geometry and topology: mapping class groups equipped with their actions on Teichmüller space, and Kleinian groups with their actions on hyperbolic space. Specifically, he hopes to answer a fundamental outstanding question in the geometry of mapping class groups: Do there exist Gromov-hyperbolic surface bundles over surfaces?