Scientists / Open questions
William P. Thurston
Low-dimensional topology; hyperbolic geometry
1982 Fields Medal
4 questions
Positive first Betti number of finite covers of random Heegaard splittings (Dunfield-Thurston Questions 4.8 and 9.2 and the non-solvable extension of Theorem 9.1)
The size of spanning disks for unknotted polygonal curves: exponential lower bound versus upper bound
Optimal label alphabets and the hypergraph/simplicial extension of the Sleator-Tarjan-Thurston derivation-encoding scheme
Chern's conjecture for closed affine manifolds and the Hopf sign conjecture: the surviving open core of the Hirsch–Thurston Euler-characteristic questions