Scientists / Open questions
Stephen Smale
Differential topology; dynamical systems
1966 Fields Medal
3 questions
Global classification of Morse-Smale gradient systems and adapted energy functions: the open core of the program announced in Smale's On Gradient Dynamical Systems (1961)
Adaptive and optimal sampling parameters for certified homology recovery of submanifolds: the deferred parameter theory of Niyogi–Smale–Weinberger (2008)
Explicit representatives of the regular homotopy classes of immersed spheres, and the classes containing embeddings (Smale's geometric problems of 1959)