As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants (nontrivial only for genus 0 and 1) of Calabi-Yau 4-folds using Gromov-Witten theory and conjecture their integrality. In this talk, we will explain how to give a sheaf theoretic interpretation of Klemm-Pandharipande's invariants using moduli spaces of stable objects in derived categories. Based on joint works with Davesh Maulik and Yukinobu Toda.

Only for Kyoto university students and staff. Please contact Iritani for participation.