Title: Projective coordinates for the analysis of data

Date: 01/12/2017

Time: 2:00 PM - 2:50 PM

Place: C304 Wells Hall

Barcodes - the persistent homology of data - have been shown to be effective quantifiers of multi-scale structure in finite metric spaces. Moreover, the universal coefficient theorem implies that (for a fixed field of coefficients) the barcodes obtained with persistent homology are identical to those obtained with persistent cohomology. Persistent cohomology, on the other hand, is better behaved computationally and allows one to use convenient interpretations such as the Brown representability theorem. We will show in this talk how one can use persistent cohomology to produce maps from data to (real and complex) projective space, and conversely, how to use these projective coordinates to interpret persistent cohomology computations.