Dr. Peer-Timo Bremer

"Large-Scale Topological Analysis: Theory and Practice"

Topological techniques have become one of the corner stones of scientific data analysis. Based on new mathematical theories and efficient streaming algorithms they allow an unprecedented level of analysis to be applied to extreme scale data which is increasingly common in a large number of scientific disciplines. In this talk I will discuss a general framework for topology based data analysis that is both highly flexible as well as efficient. I will introduce a new branch of Morse theory adapted to finite precision computations and unaffected by numerical instabilities. Furthermore, I will demonstrate how a small set of general tools based on this framework can be used to define, extract, and analyze a wide variety of features in broad collection of data sets. Finally, I will present a number of results ranging from elementary physics and material science to combustion research and uncertainty quantification enabled through topological analysis.