Moduli of Curves and Moduli of Sheaves - Relationships and Correspondences

Explore the intricate relationships between moduli spaces of curves, maps, and sheaves in this 54-minute lecture by Rahul Vijay Pandharipande. Begin with an examination of the Gromov-Witten/Donaldson-Thomas (GW/DT) correspondence proposed over two decades ago. Delve into the descendent and relative correspondences, which led to the proof of the GW/DT correspondence for the Calabi-Yau quintic. Investigate how the study of correspondences in families has played a crucial role in connecting to other fundamental moduli problems in algebraic geometry, including the moduli of K3 surfaces and abelian varieties. Gain insights into the fundamental relationships between these diverse moduli geometries, showcasing the interconnectedness of various branches of algebraic geometry.