DubTop Seminar: Filtered objects, spectral sequences, and t-structures

A recent trend in homotopy theory has been the replacement of the phrase "There is a spectral sequence..." with "There is a filtration...". This talk is an entryway into this shift. We will begin by discussing motivation for studying filtrations as opposed to spectral sequences. Then, we will introduce filtered objects and t-structures on stable \$\infty\$-categories. We will end by showing how two natural spectral sequences on a filtered object can be related.