Ziyang Gao of the Institute for Advanced Study presents research on algebraic cycles attached to curves, delivered as part of the IAS workshop on Recent Developments in Hodge Theory and O-minimality. Working in the moduli space of curves Mg, Gao constructs a Zariski open dense locus on which the Beilinson-Bloch height of the Gross-Schoen and Ceresa cycles behaves as a Weil height, meaning it admits a lower bound and satisfies the Northcott property. He explains how this construction yields a generic positivity result for the heights of these cycles, strengthening what is known about their arithmetic behavior across the moduli space. The talk is joint work with Shouwu Zhang and assumes familiarity with arithmetic geometry, height theory, and the structure of moduli spaces of curves. It is a specialist research seminar rather than an introductory lecture, aimed at mathematicians already working in arithmetic and algebraic geometry, presented at Simonyi Hall at the Institute for Advanced Study.