Zoll surfaces, invisible lenses and rigidity

I will discuss an interesting class of Riemannian metrics on the unit disc in the plane and on the 2-sphere together with some remarkable rigidity results connected with them.

No background on manifolds or geometry is needed, you just need to know about cylindrical coordinates on the 2-sphere (and polar coordinates on the disc). Riemannian metrics and geodesics (on open sets in the plane) will be briefly introduced at the beginning of the lecture.