Oblomkov, AlexeiWang, Arthur2024-12-112024-12-112024-0910.7275/55181https://hdl.handle.net/20.500.14394/55181In this thesis we develop a geometric interpretation for Rasmussen's spectral sequences using a construction for Khovanov-Rozansky link homology developed by Oblomkov and Rozansky. In the special case of Khovanov homology, we provide a proof for the geometric construction of Rasmussen's differentials by examining the relationship between matrix factorizations and Soergel bimodules. Finally we leverage the techniques developed in order to provide an alternative method for computing the Khovanov homology of knots and links.Attribution 4.0 InternationalAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/knot theory, matrix factorizations, Khovanov homology, link homologyDissertation (Open Access)https://orcid.org/0000-0003-0829-9310