Banca de DEFESA: LUCIANO HENRIQUE LACERDA DE ARAÚJO

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUCIANO HENRIQUE LACERDA DE ARAÚJO
DATE: 29/01/2024
TIME: 14:00
LOCAL: Sala 801 e https://conferenciaweb.rnp.br/sala/daniel-73
TITLE:

Persistent Homology and its interaction with Discrete Morse Theory

PAGES: 178
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SUMMARY:

In this dissertation, we present an introduction to Persistent Homology and its relationship with Discrete Morse Theory. Using this relationship, we present a strategy to simplify the calculation of Homology Groups.
In recent years, technological advancements have led to the production and accumulation of a substantial amount of data. As a result, Topological Data Analysis, an emerging field, utilizes the topological structure of this data to extract information. It proves to be particularly useful in situations where traditional methods may fail due to data complexity, multidimensionality, or the presence of outliers.
Among the techniques of Topological Data Analysis, we can highlight Persistent Homology, characterized by the use of tools from Algebraic Topology, particularly homology groups. In this text, we present the basic theory of Persistent Homology and prove one of its fundamental results: the Stability Theorem.
Finally, using Discrete Morse Theory, we introduce a strategy to simplify the calculation of homology groups. In the process of searching for a suitable Morse function, the possibility of using the Discrete Fourier Transform in the context of abelian groups arises. Thus, we present the construction of Morse-Fourier functions.

COMMITTEE MEMBERS:
Presidente - Interno ao Programa - 1574165 - DANIEL MIRANDA MACHADO
Membro Titular - Examinador(a) Interno ao Programa - 1067113 - DAHISY VALADAO DE SOUZA LIMA
Membro Titular - Examinador(a) Externo à Instituição - CARLOS HENRIQUE GROSSI FERREIRA - USP
Membro Suplente - Examinador(a) Interno ao Programa - 1675735 - MARIANA RODRIGUES DA SILVEIRA
Membro Suplente - Examinador(a) Externo à Instituição - IVAN STRUCHINER - USP