Abstract:
I will give a quick introduction to spectral sequences, how they arise, and how they can be used. I will also say something about convergence and multiplicative structure in spectral sequences. I do not plan to develop examples in the first talk, but expect to return to these later.
This is meant to give sufficient background for later talks on topological Hochschild, topological periodic, and topological cyclic homology of ring spectra, with their even and motivic filtrations, whose associated graded spectra model prismatic and syntomic cohomology.