Suter, Aiden2024-08-212024-08-212024-08-212024-07-31https://hdl.handle.net/10012/20828This thesis contains results pertaining to different aspects of the 3d mirror symmetry between Higgs and Coulomb branches. In Chapter 2 we verify the 3d A-model Higgs branch conjecture formulated in [BF23] for SQED with n > 3 hypermultiplets. The conjecture claims that the associated variety of the boundary VOA for the 3d A-model is isomorphic to the Higgs branch of the physical theory. We demonstrate that the boundary VOA is L1(psl(n|n)) and show that its associated variety is the closure of the minimal nilpotent orbit, verifying the conjecture. In Chapter 3 we build on the work of [Web19a; Web22] by explicitly constructing a tilting generator for the derived category of coherent sheaves on T∗Gr(2, 4). This variety is the Coulomb branch for a quiver gauge theory and has functions described by a KRLW algebra. We achieve this result by constructing generators for modules over this diagrammatic algebra and identifying the coherent sheaves these correspond to.enKLR algebrasRepresentation theoryVertex operator algebras3d mirror symmetryAlgebraic geometryQuantum field theoryMathematical physicsQuantum algebraDoctoral Thesis