Calendar

Global class field theory provides a universal abelian reciprocity laws for 1-dimensional global fields. It has been generalized in a number of different directions. In the geometric setting, it manifests as a duality between (different kinds of) sheaves on the moduli spaces of line bundles and 1-dimensional representations of the fundamental group of a curve. In a different direction, Kato and Saito gave a generalization to higher dimensional varieties. I will describe a categorification of the Kato-Saito higher class field theory, in which the moduli space of line bundles is generalized to the moduli space of zero cycles. This is joint work in progress with Elmanto.

These lectures will describe connections between dynamical systems and topics including algebraic geometry, number theory,
unipotent flows and fractal Jordan curves.

All talks will be for a general audience, and no talk is a prerequisite for any other.