[Topology.beta] Today in AG: Otto Sumray

[Rot, T.O. (Thomas)]

Dear all,

Today we have a semi-external speaker: Otto Sumray will speak at 11:00 in Maryam. Title and abstract below.

Best,
Thomas

 Quiver Laplacians and Data
Analysing the topology or geometry of data is a common task in data analysis, using methods such as clustering, networks, and persistent homology. Often, however, we wish to embellish data with extra local information, which mathematically can take the form of a quiver representation or cellular sheaf. One example of this enriched data comes from analysis of single-cell epigenetics, and this situation can be further abstracted to a question about local versus global feature selection.
Graph Laplacians have had great success in the analysis of networks. We introduce the quiver Laplacian as an analogue of the graph Laplacian for quiver representations, and formulate a pipeline for its application to local versus global feature selection.
Applying it to our case study in single-cell epigenetics, we show that the eigenvalues of the quiver Laplacian can aid in feature selection to recover biologically meaningful results. To show stability of this method, we provide explicit bounds on how the spectrum of a quiver Laplacian changes when the representation and the underlying quiver are modified in certain natural ways.



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