New Frontiers in Dimension Theory of Dynamical Systems – Applications in Metric Number Theory (Web)

The recent history of mathematics demonstrates that results in dimension theory and geometry combined with contemporary techniques in dynamics lead to exciting results in number theory. Examples include Furstenberg’s proof of Semeredi’s theorem, Margulis’ work on group actions on homogeneous spaces and Ratner’s work on actions of groups generated by unipotent elements which led to a solution of Oppenheim’s conjecture, as well as Lindenstrauss’ work on quantum unique ergodicity and (jointly with Weiss) on Gromov’s mean dimension.

In another direction, recent results of Hochman, Shmerkin, Solomyak, Peres and Wu on the dimension of self-similar sets and measures associated with conformal iterated function systems with overlaps introduced powerful new methods which helped settle several major open problems.

The aim of this workshop is to provide a platform for the exchange of knowledge through research talks, open-problem sessions and round-table discussions, in order to bring to light new aspects and gain new insights to these and related topics.

This event is dedicated to the celebration of Prof. Jörg Schmeling’s 60-th Birthday.