Mathematical Problems in Theoretical Physics

Lattice instantons: What they are and why they are important.- Gauge fields on the lattice.- Lattice gauge theories.- Some frontiers in constructive quantum field theory and equilibrium statistical mechanics.- New proofs of long range order.- Number of phases in one component ferromagnets.- A survey of local cohomology.- Operator algebras and statistical mechanics.- Foundations of equilibrium quantum statistical mechanics.- Unbounded derivations of C*-algebras and corresponding dynamics.- to the flow of weights on factors of type III.- The von Neumann algebra of a foliation.- Nuclearity and the C*-algebraic flip.- On the Connes spectrum of simple C*-dynamical systems.- Quantum field theory of massless particles and scattering theory.- Scattering theory in quantum mechanics and asymptotic completeness.- Static solitons in more than one dimension.- Geometry of Yang-Mills fields.- Periodic solitons and algebraic geometry.- Yang--Mills equations as inverse scattering problem.- Nonlinear evolution equations solvable by the inverse spectral transform.- Quantization of particle-like solutions in field theory.- Topics in infinite dimensional analysis.- Mathematical foundations of the renormalization group method in statistical physics.- On the renormilization group for the hierarchical model.- Fluctuationes in Curie-Weiss exemplis.- On the problem of the mathematical foundation of the Gibbs postulate ie classical statistical mechanics.- Dynamical systems with turbulent behavior.- Generic properties of Navier-Stokes equations.- A limit theorem for turbulent diffusion.- Many particle scattering aitlitudes.- A Remark on equations of motion in asymptotically free theories.- Short-distance expansion for products of current-like operators.- The use of exterior forms in field theory.- On extensions of flows in the presence of sets of singularities.- On the uniqueness of the equilibrium state for plane rotators.- A geometric approach to the solution of conformal invariant field equations.- Stability, detailed balance and KMS condition for quantum systems.- Stochasticity and irreversibility in infinite mechanical systems.- Why the KMS states?.- A comment to the talk by E. Seiler.