Abstract:
I shall speak within my lecture
about an interesting conjecture
of Eremenko from a fine
paper of 1989.

He asked if each escaping point
can to infinity be joined
using a connected shape
all points of which themselves escape.

Although quite simple it appears,
this question has for many years
caused me and others some despair,
sleepless nights and greying hair.

Through our intense investigation
of transcendental iteration,
much progress was indeed obtained,
but the conjecture, it remained -

till now! By work with Waterman
and Marti-Pete, now I can
describe to you, within my lecture,

a counterexample to Eremenko's Conjecture.