Activities This Week

We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, we find that the central value of the L-function of the relevant motive is non-vanishing, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients. This is joint work with Ari Shnidman.

Discrepancy is a measure of equidistribution for sequences of points. A bounded remainder set is a set with bounded discrepancy, that is, the number of times it is visited differs by the expected time only by a constant. We discuss dynamical, symbolic, and spectral approaches to the study of bounded remainder sets for Kronecker sequences. We consider in particular discrepancy in the setting of symbolic dynamics and we discuss the existence of bounded remainder sets for some families of zero entropy subshifts. Note that bounded discrepancy has also to do with the notion of bounded displacement to a lattice in the context of Delone sets. We focus on the case of Pisot parameters for toral translations and then show how to construct symbolic codings in terms of multidimensional continued fraction algorithms.
This is joint work with W. Steiner and J. Thuswaldner.