Persistent cohomology

• Grant number: 19/22023-9
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: January 01, 2020
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alice Kimie Miwa Libardi
• Grantee: Marco Antonio de Freitas Contessoto
• Supervisor: Roberto Facundo Memoli Techera
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Institution abroad: Ohio State University, United States
• Associated to the scholarship: 17/25675-1 - Persistent cohomology, BP.DR

Abstract

One of the recent trends in the Applied Algebraic Topology field has been the development of algorithmic techniques that can efficiently compute the persistence barcodes associated with a given simplicial tower K. There are very recent indications that ideas related to cohomology often lead to algorithms that present higher memory efficiency and lower overall computational complexity in practical applications. At the same time, there are only isolated attempts to harnessing the full power of cohomological ideas.The objective of this work is to investigate the intersection between persistence and cohomological ideas and using the tools of applied algebraic topology to develop the theoretical machinery in persistent cohomology and also to explore the algorithmic and computational concepts. (AU)