Isaac Ren: Using spectral sequences to replace kernels with cokernels

One object that I study in my research is a chain complex of kernels of linear maps. In particular, I want to efficiently compute its homology. This can be done, but for reasons that I will explain in this talk, we can do (slightly) better by replacing the kernels with cokernels.

After a brief presentation of the context of these chain complexes, I will introduce spectral sequences as a tool to replace the kernels of the chain complex by cokernels. I will explain why, in theory, cokernels are better than kernels and present, in practice, some numerical results. No knowledge of spectral sequences is required for this talk; awareness of basic linear algebra is enough.