On transport twistor spaces (Joint with IP seminar)

For 2-dimensional Riemannian manifolds there is a rich
interplay between the geodesic transport equation on the unit tangent
bundle and Fourier analysis in the vertical fibres. This interplay has
shaped the understanding of many geometric inverse problems and
rigidity questions since the late 1970s. The transport twistor space
is a (degenerate) complex 2-dimensional manifold Z which encodes this
interplay and sheds new light on numerous aspects of the transport
equation by translating them into a complex geometric language. The
focus of the talk will lie on these novel twistor correspondences, as
well as some new results regarding the algebra of holomorphic
functions on Z and its moduli space of holomorphic vector bundles.
This is based on joint work with Thibault Lefeuvre and Gabriel
Paternain.