Scientists / Open questions
Henri Poincaré
Dynamical systems; topology; celestial mechanics
5 questions
Poincaré's 1883 tangent conjecture for the limit curve of second-family Kleinian groups (necklace groups)
Poincaré's 1884 program on linear equations with algebraic coefficients: effective determination of the accessory parameters of the uniformizing second-order Fuchsian equation for general types, and the unproven convergence criterion for his series construction (Poincaré, 1884)
Structure and conjugacy classification of infinitely generated Fuchsian groups — the class Poincaré set aside in 1882
Higher-order analogues of Fuchs' fixed-branch-point conditions and an effective Fuchsian method for the moduli of a Riemann surface
Poincaré's program for polarization by diffraction: a quantitative theory of edge rounding (arris) and finite conductivity reconciling Gouy's experimental laws — the equal-angle intensity maximum, the inter-polarization phase difference, and spectral coloration