# Helge Gloeckner

## Open problems in the theory of infinite-dimensional Lie groups

In a preprint from 1982 preceding his well-known article
from 1983, John Milnor discussed the foundations of the
theory of infinite-dimensional Lie groups and formulated
several fundamental problems, which are still beyond reach today. In the talk, I'll report on recent partial progress.
In particular, I'll sketch why Hoelder continuous homomorphisms between infinite-dimensional Lie groups are
smooth. Milnor's original question whether every continuous
homomorphism is smooth remains open.