English

Introduction to arithmetic groups

-what is a locally symmetric space; geometric meaning of R-rank and Q-rank; brief summary; basic properties of lattices; what is an arithmetic group; examples of arithmetic groups; SL(n,Z) is a lattice in SL(n,R); real rank; Q-rank; quasi-isometries; unitary representations; amenable groups; kazhdan's property T; ergodic theory; mostow rigidity theorem; margulis superrigidity theorem; normal subgroups of gamma; arithmetic subgroups of classical groups; construction of a coarse fundamental domain; ratner's theorems on unipotent flows; basic facts about semisimple lie groups; assumed background; a quick look at S-arithmetic groups-

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