Topological data analysis

• Grant number: 15/16255-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 19, 2015
• End date: October 22, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Alice Kimie Miwa Libardi
• Visiting researcher: Roberto Facundo Memoli Techera
• Visiting researcher institution: Ohio State University, Columbus, United States
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

Topological data analysis (TDA) has emerged as a promising approach to many of the aforementioned problems. Persistent homology was introduced heuristically by computer scientists about fifteen years ago, but in the last decade TDA has experienced vigorous development both on the theoretical and applied fronts, mainly through multidisciplinary efforts involving math-ematicians, statisticians, computer scientists and domain experts. Notwithstanding these early successes, many important problems, ramifications and applications still remain to be explored. As a matter of fact, TDA in many ways still is in its infancy. In Brazil, presently there is no research activity in TDA, so this timely project intends to plant a seed and start to cultivate this area that is likely to have a significant long-term impact in a broad range of disciplines. There is a community of Brazilian topologists and students interested in these developments. The primary goals of this project are: (i)to introduce TDA to graduate students and researchers in Brazil and (ii)to establish long-term research collaborations with institutions in the USA that have focused ongoing efforts in this line of work. To achieve the first goal, we propose a mini-course on TDA comprising a series of lectures by Prof. Facundo Memoli, a mathematician at Ohio State University who hasa multidisciplinary background and is a leading expert on the subject. The proposed lecture series will start from basic material on persistent homology, progressing to the theoretical foundations of the methods used, proofs of stability and robustness of persistent homology to sampling, noise and outliers, and applications to problems in shape and image analysis. The lectures will be complemented by tutorials, where Prof. Memoli will coordinate hands-on activities with the open source software package JavaPlex for computation of bar codes and persistence diagrams, and the bottleneck distance between these topological invariants. In parallel with the minicourse, there will be intensive discussion of open problems in the area with the goal of establishing this line of research in Brazil and set the foundations for future collaborations. (AU)