Table of Contents:
  • Why are geometric representations interesting?
  • Planar graphs
  • Rubber bands
  • Discrete harmonic functions
  • Coin representation
  • Square tilings
  • Discrete analytic functions
  • Discrete analytic functions: Statistical physics
  • Adjacency matrix and its square
  • Orthogonal representations: Dimension
  • Orthogonal representations: The smallest cone
  • Orthogonal representations: Quantum physics
  • Semidefinite optimization
  • Stresses
  • Rigidity and motions of frameworks
  • The Colin de Verdie��re number
  • Metric representations
  • Matching and covering in frameworks
  • Combinatorics of subspaces