### Carleman estimates for geodesic X-ray transforms.

Ergodic Theory and Dynamical Systems Seminar

22nd March 2018, 3:00 pm – 4:00 pm

Howard House, 4th Floor Seminar Room

I will describe a new energy estimate for the geodesic vector field

of a manifold of negative curvature. The estimate has several

applications including

injectivity of non-abelian X-ray transforms and the existence of

invariant distributions with prescribed first Fourier coefficients

for the geodesic flow. This is joint work with Mikko Salo.

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