**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.