# Oliver Gäfvert: Topological Data Analysis, Statistics and Machine Learning

**Time: **
Mon 2019-02-18 10.00 - 12.00

**Lecturer: **
Oliver Gäfvert, KTH

**Location: **
Room 3418, math department KTH, floor 4 (bottom floor)

Abstract: The talk will consist of two parts. In the first part I will define a class of metrics on multiparameter persistence modules facilitated by the introduction of persistence contours. Using these, we can compute the stable rank, an invariant which could previously not be computed, and show that it's in general NP-hard to compute. Moreover, persistence contours can be used to put persistence modules in a machine learning context by providing a class of metrics that can be optimized over. This could for instance be used to solve classification problems in a metric learning sense, called contour learning. In the second part I will discuss computations and implementations of computing persistence modules and contour learning.