HILBERT'S 23 PROBLEMS
Paris, 1900
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SOLVEDPARTIALLY SOLVEDOPENTOO VAGUE
#21
SOLVED
Monodromy and Linear Differential Equations
Plemelj (1905), Bolibruch (1989) (1905/1989)
Does there exist a Fuchsian system of linear ODEs with a prescribed monodromy group?
HISTORY
Plemelj claimed a positive answer (1905). Bolibruch (1989) found a counterexample: the answer is sometimes no. The full picture is now understood.
Revealed deep connections between differential equations, algebraic geometry, and representation theory.
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