Nonstandard methods in Lie theory
Abstract: In this talk, I will survey several applications of nonstandard methods in Lie theory. I will first describe the nonstandard solution to Hilbert's fifth problem due to Hirschfeld and my extension of this approach to the setting of local groups, including a couple of recent applications of this latter result. I will then discuss Pestov's construction of nonstandard hulls of Banach-Lie groups with an application to enlargeability of Banach-Lie algebras. Finally, I will present two generalizations of Pestov's construction: a nonstandard hull construction for locally exponential Lie groups and algebras and a nonstandard hull construction for locally uniform groups. The latter construction is work in progress and involves an interesting interplay between the theory of infinite-dimensional groups and the theory of local groups.
Friday January 20, 2012 at 3:00 PM in SEO 636