Title: TOPOLOGICAL NOVELTY IN "PERSISTENCE" FOR ANGLE VALUED MAPS, "JORDAN CELLS" (definitions and calculations)
Speaker: Dan Burghelea (The Ohio State University)
Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html
Abstract: Some geometrization of DATA leads to a nice space (finite simplicial complex) equipped with an angle valued map. For such space and map, in order to describe the changes in the homology of the levels, " topological persistence theory " provides, in addition to "bar codes", a collection of mathematical objects called "Jordan cells".
I will explain the definition and the calculation of these "Jordan cells" based on a less familiar but still elementary piece of linear algebra, the theory of linear relations. This presentation provides also an alternative computational description of a topological invariant known as "Alexander polynomial " of a knot , and of some of its generalizations.
