RJ Lipton conjectures a link between group growth theory and complexity theory. Group growth theory has undergone rapid advance in the last decade and has many surface similarities/ parallels with complexity theory. (of course there are other deep known links between TCS/ group theory.)
has anyone seen a link between group growth theory and complexity theory? eg have any complexity class separations been found expressible in this framework, etc?
(eg conceivably there could be an intermediate link via boolean circuits etc.)