[Topology.beta] CTAAAG tuesday

[Rot, T.O. (Thomas)]

Dear all,

Samuel is going to talk about his research. See abstract and title below. The format has slightly changed. Talks will be about an hour, with time for questions after.

Are there any other PhD students that want to discuss their research the coming weeks?

Best,
Thomas


AG:10-06-2025: Samuel: Spectral systems and connection matrices
Spectral sequences and systems are tools from algebraic topology widely known and used in the study of homology and fibrations. These usually arise form an exact couple system, having a filtration on a space associated.
Parallel to this, connection matrices were developed in the realm of applied topology for qualitative study of dynamical systems. We have a Morse decomposition of a system, and the relative homologies being the Conley index provide us information about it. These two wildly different ideas turn out to be two faces of the same coin. We see how these connection matrices are at its core just a spectral system, and how given an exact couple system one can build a connection matrix and thus a space that generates it with the relative homologies.

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