Speaker: Kimball Martin (Osaka Metropolitan University)

Title: Rationality questions for genus 2 curves with real multiplication

Abstract: Genus 2 curves can be broadly classified by the endomorphisms of their Jacobians.  For a generic curve, the endomorphism ring is Z.  If the endomorphism ring contains a real quadratic order, we say the curve has real multiplication.  I will discuss the problems of classification and construction of such curves over C (classical) and over Q (new).  I will contrast this with the case of elliptic (genus 1) curves, and discuss the connection with modular forms.  This is joint work with Alex Cowan and Sam Frengley.