Exceptional sets play an important role in numerous branches of mathematics, for instance in measure theory, topology, harmonic and complex analysis, Banach space theory, algebraic geometry, combinatorics, probability and ergodic theory, set theory and descriptive set theory, just to mention a few. Exceptional sets describe notions of smallness from various points of view, some notable examples are the countable sets, null sets of a measure, meager sets, sets of zero analytic capacity in complex analysis, non-stationary sets in set theory, Gaussian or Aronszajn or cube null sets in Banach spaces, Haar null sets in the sense of Christensen in Polish groups, as well as various ideals on the natural numbers, for example the sets of zero asymptotic density.

These notions have numerous applications to all the areas mentioned above, as well as to the structure of Polish groups and to the theory of Polish group actions.

The analysis of exceptional sets naturally leads to problems of descriptive set theoretic nature. On the one hand, regularity properties of the exceptional sets are often handled by methods of descriptive complexity, and on the other hand, in the investigation of ideals on the natural numbers the descriptive complexity of the ideal itself plays a central role.

The goal of this workshop is to bring together experts from various fields related to exceptional sets and discuss the recent developments.

These notions have numerous applications to all the areas mentioned above, as well as to the structure of Polish groups and to the theory of Polish group actions.

The analysis of exceptional sets naturally leads to problems of descriptive set theoretic nature. On the one hand, regularity properties of the exceptional sets are often handled by methods of descriptive complexity, and on the other hand, in the investigation of ideals on the natural numbers the descriptive complexity of the ideal itself plays a central role.

The goal of this workshop is to bring together experts from various fields related to exceptional sets and discuss the recent developments.