Addington, NicolasTakahashi, Ryan2020-09-242020-09-242020-09-24https://hdl.handle.net/1794/25661We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, a global version of an action studied by Cautis, Kamnitzer, and Licata. As a corollary, we find that the moduli spaces in this sequence which are birational are also derived equivalent.en-USAll Rights Reserved.Electronic Thesis or Dissertation