Special Colloquium
Isaac Goldbring
UCLA
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