Title: Zooming into Catalan's conjecture.
Abstract: We give a historically motivated
introduction to the study and
solution of Catalan's conjecture - which consists in the statement that
the only consecutive perfect powers are 8 and 9.
In the first part of the talk, we will give a historical overview of the
various approaches - and respective results - to the study of Catalan's
conjecture. In the second part, the zooming in will consist in an
increasingly technical, magnifying focus on the central consequences of
the presumable existence of unknown solutions to Catalan's equation. The
way these consequences lead to a contradiction should become clear or at
least plausible to the audience (depending upon time, technical
prerequisites ... and, maybe, chemistry of the moment).