Banca de DEFESA: RAFAEL DOS SANTOS CAVALCANTI

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE: RAFAEL DOS SANTOS CAVALCANTI
DATA : 29/05/2026
HORA: 10:00
LOCAL: Google Meet
TÍTULO:

Topological Data Analysis in Finsler Spaces

PALAVRAS-CHAVES:

Finsler Metric, Topological Data Analysis, Simplicial Complex, Persistent Homology

PÁGINAS: 49
RESUMO:

We introduce a novel framework for Topological Data Analysis (TDA) based on Finsler geometry, enabling the incorporation of directional, asymmetric, and context-dependent information into topological constructions. Within this setting, we generalize the classical Vietoris–Rips and ˇCech complexes and introduce a new simplicial complex that captures richer pairwise interactions beyond standard distancebased relations. We establish fundamental geometric and topological properties of the resulting filtrations, including convexity, contractibility, and stability of persistence diagrams. Furthermore, we show that several information-theoretic approaches to TDA, such as those arising from Burg and Fisher metrics, are naturally recovered as special cases of our Finslerian framework, providing a unifying geometric perspective

MEMBROS DA BANCA:
Externo à Instituição - MATHIEU DESROCHES
Externo à Instituição - IOAN BUCATARU
Interno - 1394531 - ALCIDES DE CARVALHO JUNIOR
Externo à Instituição - FERNANDO ANTONIO NOBREGA SANTOS
Externo à Instituição - SERAFIM RODRIGUES