This award provides partial support for a four-day international conference to cover recent progress and developments of the theory of Lie groups, discrete subgroups and homogeneous spaces. The last three decades have brought spectacular advances in the area, highlighting various connections to dynamical systems and ergodic theory, Diophantine approximation, rigidity theory, discrete mathematics etc. The progress has been especially rapid and impressive during several recent years. However, no major international conferences unifying this subject and related fields were held since the beginning of the 21st century. This justifies the need for the planned conference, which is going to bring together world leaders in these fields and serve as a forum for dissemination of new results, methods and ideas. Tentative list of topics includes: rigidity and classification of actions of higher rank Lie groups and lattices; ergodic theorems for lattice actions; growth properties of linear groups and Tits alternative; counting integer points on homogeneous varieties; measure rigidity of higher rank abelian actions and quantum unique ergodicity; the set of exceptions to Littlewoods conjecture; applications to Diophantine approximation with dependent quantities; invariant measures for actions on the Teichmueller space and applications to billiards.
