Title: Trouble with Eremenko's conjecture
Author: Lasse Rempe


I shall speak within my lecture
Of an interesting conjecture
Made by Alex in a fine
Paper of nineteen eighty nine.

He asked if each escaping point
Can to infinity be joined
Using a connected shape,
All points of which themselves escape.

This question may be simply stated,
But it should not be underrated
For many challenges remain.
Why this may be I shall explain.

Oberwolfach, December 7, 2009. Workshop "Escaping set in transcendental dynamics".