This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang–Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory.

Contents:

• Yangian and Applications (C-M Bai et al.)
• The Hypoelliptic Laplacian and the Chern–Gauss–Bonnet (J-M Bismut)
• S S Chern and Chern–Simos Terms (R Jackiw)
• Localization and Conjectures from String Duality (K F Liu)
• Topologization of Electron Liquids with Chern–Simons Theory and Quantum Computation (Z H Wang)
• Topology and Quantum Information (L H Kauffman)
• Toeplitz Quantization and Symplectic Reduction (X N Ma & W P Zhang)
• Murphy Operators in Knot Theory (H R Morton)
• Separation Between Spin and Charge in SU(2) Yang–Mills Theory (A J Niemi)
• Löwner Equations and Dispersionless Hierarchies (K Takasaki & T Takebe)
• and other papers