The Bulletin of the AMS is going to publish a 57-page survey on growth in groups, which is already online, and which touches several topics of interest to readers of in theory, including the recent work of Bourgain and Gamburd on expander Cayley graphs of 
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❗ wow nice/ great find thx for sharing!
💡 rjlipton thinks there may be some connection of group growth theory to algorithmic complexity theory ie maybe separations of complexity classes. do you know of any papers that make connections? have long wondered if it might be possible thru circuit theory where somehow elements of the group represent circuit gates etc…. feel there could be some big bridge thm here somewhere….