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Path geometries, Fourier modes and holomorphic curves

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Thomas Mettler
Universität Frankfurt
Thu, 2019-06-13 16:30 - 17:30
MPIM Lecture Hall

A path geometry on a surface M prescribes an immersed path for every
direction in each tangent space of M. Fixing a Riemannian metric g on M, a
path geometry can be encoded in terms of a real-valued function f on the
unit tangent bundle of (M,g). Requiring the paths to agree with the
geodesics of some connection is equivalent to the condition that the
vertical Fourier expansion of f contains only terms of degree 1 and 3. I
will relate the vanishing of these Fourier modes to (pseudo-)holomorphic
curves and discuss related PDE problems. Joint with Gabriel Paternain.

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