Phase Transitions in Physics, Computer Science, Combinatorics and Probability Theory

August 21 to August 25, 2006

at the

American Institute of Mathematics, Palo Alto, California

organized by

Persi Diaconis, Daniel Fisher, Cris Moore, and Charles Radin

This workshop, sponsored by AIM and the NSF, will be devoted to the study of phase transitions in several traditionally separate subjects.

Phase transitions have been an important part of statistical mechanics for many years. More recently phase transitions have become a hot topic in computer science (study of 3-satisfiability), combinatorics (birth of the giant component for various random graph models) and probability theory (cutoff phenomena for markov chains). We propose to bring together experts within each area to present the various intuitions, motivations, canonical examples and conceptual techniques of their areas, the hope being to come to agreement on a few key definitions, and perhaps thereby to bring fresh ideas to bear on open problems.

Examples of topics for discussion/open problems:

  1. Various definitions of phase transitions.
  2. Proof of a solid/fluid phase transition, for instance in the hard sphere or hard disk model, or related nonequilibrium models of granular materials.
  3. Proof of a rigorous connection between the birth of a giant component in random graph theory, and of the cutoff phenomenon for markov chains.
  4. Proof of a sharp phase transition for the algorithmic K-SAT problem, for K > 2.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

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