(1)Geometric constraints (declarative geometry) and its applications to: molecular structure and interaction, virus geometry, assembly pathways, geometric and kinematic mechanisms, solid modeling and assembly. (2) Self-organizing and game theoretic mechanisms and their applications to biology, the internet. (3) Complexity (computational/descriptive/physical): lower bounds, derandomization, compressibility, information, learnability, approximability, sampling; (4) Geometric and Algebraic complexity. (5) Computational Geometry (6) Discrete modeling and algorithms.