Session S27 - Categories and Topology

Wednesday, July 21, 18:30 ~ 19:00 UTC-3

Adjoint functors and symmetric monoidal categories for topological data analysis

Peter Bubenik

University of Florida, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Persistent homology is an important tool in topological data analysis, whose goal is to quantify and learn from the `shape' of data. First we encode scientific data as a diagram of spaces and then we apply a homology functor to obtain a diagram in an abelian category. In nice cases, this diagram can be represented by a formal sum in a pointed metric space. I will show how categorical constructions give us a family of distances on these formal sums.

Joint work with Alex Elchesen (University of Florida, USA).

View abstract PDF