Video Lectures

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We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical “quadratic” point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue’s result, that this point is...

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat 3-manifolds which we call translation prisms. Using ideas of Furstenberg, and Veech, we connect results about weak mixing properties of flows on...