Scholarship 17/25675-1 - Cohomologia, Homologia - BV FAPESP
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Persistent cohomology

Grant number: 17/25675-1
Support Opportunities:Scholarships in Brazil - Doctorate
Start date until: May 01, 2018
End date until: August 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Alice Kimie Miwa Libardi
Grantee:Marco Antonio de Freitas Contessoto
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
Associated scholarship(s):19/22023-9 - Persistent cohomology, BE.EP.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 coomology 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)

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
CONTESSOTO, Marco Antonio de Freitas. Some persistent cohomology invariants and an axiomatic version of persistent homology. 2021. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.

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