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Abstract

It is a classical result from 19th century algebraic geometry that every smooth cubic surface contains exactly 27 lines. Keeping track of the lines as one follows closed loops within the family of smooth cubic surfaces gives rise to a notion of monodromy.

At the same time, in the theory of linear ODEs, certain spaces of monodromy data can naturally be interpreted as affine cubic surfaces or related Del Pezzo surfaces.

Putting the two together, one is led to the question what the meaning of monodromy of monodromy is. In this talk, I will unpack this riddle, which in particular yields a surprising twist to a problem commonly thought of as settled in the theory of Painlevé equations.