Date & Time: July 21-22, 2014, 16:30-17:30.
Venue: Ramanujan Hall

Speaker: M. S. Raghunathan, IIT Bombay

Title: Discrete subgroups of Lie groups

Abstract: The fundamental theorem of correspondence between Lie sub-groups of a Lie group G and Lie sub-algebras of the Lie algebra Lie G of G goes a long way in helping us understand structural properties of connected closed subgroups of G. This device is evidently not available for the study of discrete subgroups and somewhat different methods are needed for their study. In the two talks I will be giving, I will outline some results about discrete subgroups in Lie Groups. Most of the attention will be directed at "lattices", i.e. discrete subgroups H in G such that G/H carries a finite G-invariant measure. Even the existence of lattices in a given Lie group is not an easy question to resolve. We will exhibit some examples which itself involves some delicate and beautiful mathematics.