Symmetries and Overdertemined Systems of Partial Differential Equations

Overdetermined Systems, Conformal Differential Geometry, and the BGG Complex.- Generalized Wilczynski Invariants for Nonlinear Ordinary Differential Equations.- Notes on Projective Differential Geometry.- Ambient Metric Construction of CR Invariant Differential Operators.- Fine Structure for Second order Superintegrable Systems.- Differential Geometry of Submanifolds of Projective Space.- Pseudo-Groups, Moving Frames, and Differentials Invariants.- on Geometric Properties of Joint Invariants of Killing Tensors.- Hamiltonian Curve Flows in Lie Groups G(U (N) and Vector NLS, Mkdv, Sine Gordon Soliton Equations.- Conformal Killing Spinors and the Holonomy Problem In Lorentzian Geometry-A Survey of New Results.- Projective Type Differential Invariants for Curves and their Associated PDES of KDV Type.- Algebraic Construction of the Quadratic First Integrals for A Special Class of Orthogonal Seperable Systems.- Geometry of Non-Regular Separation.- Higher Symmetries of the Square of the Laplacian.- Metric Connections in Projective Differential Geometry.- Exterior Differential Systems With Symmetry.- Partially Invariant Solutions to Ideal Magnetohydrodynamics.- Invariant Prolongation and Detour Complexes.- Inhomogenous Ambient Metrices.- Pfaffian Systems of Frobenius Type and Solvability of Generic Overdetermined PDE Systems.- Exact and Quasi-Exact Solvability of Second order Superintegrable Quantum Systems.- A Remark on Unitary Conformal Holonomy.- Polynomial Associative Algebras for Quantum Superintegrable Systems with A third Order Integral of Motion.- Separation of Variables for Systems of First-Order Partial Differential Equations and The Dirac Equation in Two-Dimensional Manifolds.- Differential Systems Association with Tableaux Over Lie Algebras.- Conformal Structirues with Explicit Ambient Metrics and Conformal G2 Holonomy.- Deformations of Quadratic Algebras, the Joseph Ideal for Classical Lie Algebras, and Special Tensors.- Analogues of the Dolbeault Complex and the Separation of Variables.- List of Workshop Participants.