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.

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