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1. Painlevé Property

    1. Problem 1.1.

      Given an equation with a Painlevé property, how does one identify which linear system it is?
        • Problem 1.2.

          Can one solve the above for discrete Painlevé? (If one has a nonlinear difference equation that one suspects may be Painlevé, can one work out which it is?)
            • Problem 1.3.

              Can one do 1.1 for discrete Painlevé?
                • Problem 1.4.

                  How does one check the Painlevé property?
                    1. Remark. [Peter Clarkson] Use the Ablowitz-Ramani-Segur algorithm [M.J. Ablowitz, A. Ramani & H. Segur, "A connection between nonlinear evolution equations and ordinary differential equations of P-type. I", J. Math. Phys., 21 (1980), 1006-1015]
                        • Problem 1.5.

                          In general, is there a classification of determinants that matches that for Painlevé?
                            • Problem 1.6.

                              Are the spacing distributions of the exceptional groups related to Painlevé?
                                  Answer in Chapter 8 of P. Forrester
                                • Problem 1.7.

                                  Is there an integrable structure related to general $\beta$-ensembles?

                                      Cite this as: AimPL: Painleve equations and their applications, available at http://aimpl.org/painleveapp.