What are the slopes of periodic billiard paths in a regular polygon? We will connect this question and others to:
cusps of thin groups,
curves on Hilbert modular varieties,
heights from Jacobians with real multiplication, and
a spectral gap for the Galois orbits of triangles.
Along the way we will encounter issues of chaos and decidability, first appearing in polygons with 7 and 12 sides.
Curtis McMullen (Harvard University)
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29 сен 2024
