Program:
March 10-15-17-22-24-29-31
April 5-7-12-14-19

Content:
(a) Introduction
(b) The Generalized Symmetry Method for Differential Difference Equations
    i.    Generalized Symmetries and Conservation Laws
    ii.   First Integrability Condition
    iii. Formal Symmetries and Further Integrability Conditions
    iv.   Formal Conserved Density
      A. Why Integrable Equations on the Lattice are Symmetrical
    v.    Discussion of the Integrability Conditions
      A. Derivation of Integrability Conditions from the Existence of Conservation Laws
      B. Explicit Form of the Integrability Conditions
      C. Construction of Conservation Laws from the Integrability Conditions
      D. Left and Right Order of Generalized Symmetries
    vi.   Hamiltonian Equations and their Properties
    vii. Discrete Miura Transformations and Master Symmetries
    viii. Remarks on Generalized Symmetries for Systems of Lattice Equations. Toda Type Equations
    ix.   Integrability Conditions for Relativistic Toda Type Equations
(c) Classification Results
    i.    Volterra Type Equations
      A. Examples of Classification
      B. Lists of Equations, Transformations and Master Symmetries
    ii.   Toda Type Equations
    iii. Relativistic Toda Type Equations
      A. Non-point Connection between Lagrangian and Hamiltonian Equations, and Properties of Lagrangian Equations
      B. Hamiltonian Form of Relativistic Lattice Equations
      C. Lagrangian Form of Relativistic Lattice Equations
      D. Relations between the Presented Lists of Relativistic Equations
      E. Master Symmetries for Relativistic Lattice Equations
(d) Explicit Dependence on the Discrete Spatial Variable n and the Time t
    i.    Discussion of the General Theory
    ii.   Dependence on n in Volterra Type Equations
      A. Discussion of the General Theory
      B. Examples
    iii. Toda Type Equations with an Explicit n and t Dependence
    iv.   Example of the Relativistic Toda Type
(e) Other Types of Lattice Equations
    i.    Scalar Evolutionary Discrete Differential Equations of an Arbitrary Order
    ii.   Multi-component Discrete Differential Equations
(f) Completely Discrete Equations
    i.    Introduction
    ii.   Generalized symmetries for partial difference equations and integrability conditions
    iii. Differential operators and its applications to the solution of the integrability Conditions
    iv.   Testing the integrability and some classification results
    v.    Construction of higher order symmetries for discrete equations
    vi.   Volterra type differential difference equations and the ABS classification

info: http://matem.anrb.ru/en/yamilovri