Information geometry and applications

• Grant number: 21/12253-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2022
• End date: July 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Henrique Grossi Ferreira
• Grantee: Gabriel dos Reis Trindade
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal is to introduce the central aspects of Information Geometry and its major tools. At the same time, we expect to analyze these tools in the context of some classic geometries (hyperbolic, Fubini-Study, de Sitter, anti-de Sitter) and to explore the role of Information Geometry in such environment. Finally, we expect the applicant to understand some important applications of information geometry to statistics, time series, and to the study of the state space of qbits in quantum mechanics.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

TRINDADE, Gabriel dos Reis. From statistical models to α-connections: an overview of information geometry. 2023. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.