Scientists / Open questions

Hermann Weyl

Differential geometry; representation theory; mathematical physics

10 questions

Completing Weyl's reduction theory for arithmetical equivalence: optimal constants and the structure of the reduction-cell pattern
Sequences whose dilations are uniformly distributed modulo one for every irrational number: the exceptional set of Weyl's metric equidistribution theorem
Optimal constants in the Mahler–Weyl reduced-basis inequalities for lattices and symmetric convex bodies (Weyl 1942)
The in-the-large completion of Weyl's geodesic-field sufficiency theory for multiple integrals: global embedding of extremals and global solvability of the Legendre-Riccati system
Weyl's 1922 problem of space: a constructive proof of the uniqueness of the Pythagorean measure determination, and an explanation of the world's four dimensions and metric signature (3,1)
Complete classification of the solution set of Weyl's boundary-layer problem $(A_\lambda)$ (the Falkner–Skan equation) for $\lambda > 1$
The Born-Weyl quantization of field equations: a covariant, polymomentum-based quantization reproducing canonical commutation relations and the standard probabilistic interpretation
Natural derivability of Axiom IV, subgroup restriction, and hidden invariant sets in Weyl's 1949 axiomatic theory of almost periodic vectors
The gravitational two-body problem in general relativity after Bach and Weyl (1922): exact dynamics of two attracting masses and physically acceptable static equilibria
The Riemann–Schottky problem: which principally polarized Abelian varieties (equivalently, which Riemann matrices) arise from Riemann surfaces

Back to open problems

Completing Weyl's reduction theory for arithmetical equivalence: optimal constants and the structure of the reduction-cell pattern

Sequences whose dilations are uniformly distributed modulo one for every irrational number: the exceptional set of Weyl's metric equidistribution theorem

Optimal constants in the Mahler–Weyl reduced-basis inequalities for lattices and symmetric convex bodies (Weyl 1942)

The in-the-large completion of Weyl's geodesic-field sufficiency theory for multiple integrals: global embedding of extremals and global solvability of the Legendre-Riccati system

Weyl's 1922 problem of space: a constructive proof of the uniqueness of the Pythagorean measure determination, and an explanation of the world's four dimensions and metric signature (3,1)

Complete classification of the solution set of Weyl's boundary-layer problem (Aλ)(A_\lambda)(Aλ​) (the Falkner–Skan equation) for λ>1\lambda > 1λ>1

The Born-Weyl quantization of field equations: a covariant, polymomentum-based quantization reproducing canonical commutation relations and the standard probabilistic interpretation

Natural derivability of Axiom IV, subgroup restriction, and hidden invariant sets in Weyl's 1949 axiomatic theory of almost periodic vectors

The gravitational two-body problem in general relativity after Bach and Weyl (1922): exact dynamics of two attracting masses and physically acceptable static equilibria

The Riemann–Schottky problem: which principally polarized Abelian varieties (equivalently, which Riemann matrices) arise from Riemann surfaces

Complete classification of the solution set of Weyl's boundary-layer problem $(A_\lambda)$ (the Falkner–Skan equation) for $\lambda > 1$