graduate at Matemática from Faculdade Estadual de Filosofia Ciências e Letras de Jacarezinho (1969), master's at Mathematics from Universidade de São Paulo (1976) and ph.d. at Mathematics from Universidade de São Paulo (1986). Has experience in Mathematics, focusing on Algebric Topology, acting on the following subjects: bordismo normal, normal bordism, grupo fundamental, homotopia and immersion. (Source: Lattes Curriculum)
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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, statistici…
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Let M be a smooth connected Hausdorff manifold of dimension n. We denote by TpM the tangent space of M, in p of M, by tauM the fibre bundle of M and by TM , the total space of such fibre bundle. A vector field is a continuous map M to TpM which associates to each point p of M, a vector v(p) in TpM. Then a vector field is a section v : M to TpM. Sankaran presents a very interesting surve…
This main goal of this project is to study concepts and techniques of Algebraic Topology which will give a solid background to a student who intend to do a graduate school in this area. The student already developed, under my supervision, the following topics: fundamental group, singular homology and make calculations, by using Mayer-Vietoris sequence. This project will focus on more ad…
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 pr…
(Only some records are available in English at this moment)
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 …
In the paper "Barcodes: the persistent topology data" is presented the primary mathematical tool considered in a homology theory for point- cloud data sets (persistent homology) and a novel representation of this algebraic characterization (barcodes) and in "Persistent Homology - a survey" is given a short history of persistent homology and present its basic concepts. (AU)
The theory of the Thoma factor-representations and representations of the bisymmetric groupwere considered as a limit of the classical representation theory. In the work of Neretin there was observed that a multiplication of double cosets and a multiplicativity theorem are highly general phenomena for infinite-dimensional groups. The main obstacle was a description of double cosets, which…
| 15 / 4 | Completed research grants |
| 22 / 14 | Completed scholarships in Brazil |
| 3 / 3 | Completed scholarships abroad |
| 40 / 21 | All research grants and scholarships |
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