#
Effective Randomness

August 7 to August 11, 2006
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Denis Hirschfeldt and Joseph Miller

## Original Announcement

This workshop will bring together researchers who have studied effective randomness
at different times, with different motivations, and drawing from
different academic backgrounds, with an aim toward increasing
communication and collaboration, and developing broad shared research
goals and a coherent research community.
Topics for the workshop will include effective notions of randomness
such as Martin--Löf randomness; measures of relative randomness;
effective dimension; Kolmogorov complexity and other concepts from
algorithmic information theory; and interactions with computability
theory and complexity theory.

We hope the discussions at this workshop will help us move closer to the
solution of open problems such as the ones detailed in the recent paper
Randomness and computability: open questions by Miller and Nies.
Examples of such open problems include the power of computable
nonmonotonic betting strategies, and the possible interactions between
Turing degrees of K-trivial sets, Martin-Löf random sets, and sets of
positive effective dimension. We also hope that bringing together such a
diverse group will uncover new questions and lines of research that may
help define the future of this area. Speculative interdisciplinary
questions include whether definitions of "usefulness of information"
obtained in the context of complexity theory have interesting analogs in
computability theory, and whether an effectivization of the Haar null sets
from descriptive set theory would provide a useful notion of effective
randomness in general Polish groups.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

The randomness Wiki.