Research Interests

I'm interested in and would like to work on more things than I've had the time to work on so far. At a high level, I'm interested in understanding the nature of computation and the nature of complex systems. For more details of some of the things I've worked out, check out my publications.

• The structure of algorithms and algorithmic problems
  • Computational complexity
  • Algebraic, topological, and geometric sources of computational complexity
• The relationship between information and computational complexity.
  • Kolmogorov complexity (aka algorithmic information theory) and algorithmic randomness
  • The flow of information is laid bare in the studies of data structures, succinctness, and circuit complexity
  • This relationship is particularly explicit in quantum computation, which also has a nice geometric structure
  • Information theory and the geometry of information. Coding theory. Cryptography.
• The structure and dynamics of complex systems
  • Applications of coarse geometry, graph theory, and algebraic topology to complex systems
  • Applying the theory of complex systems to actual complex systems arising in biology, ecology, energy, and economics
  • The relationship between dynamics on networks and the dynamic growth of networks
  • How local properties affect global network structure
  • How local properties affect global dynamics
  • Algorithms for complex networks