Geometry and information

Início: 06/05/2022 17:00

Término: 06/05/2022 18:00

Palestrante: Sueli I. R. Costa (University of Campinas - Brazil)

E-mail do Palestrante: sueli@unicamp.br

Resumo: In this talk it will be presented an introduction and some recent developments in two topics of Geometry we have been working which have applications in Communications: Lattices and Information Geometry. Lattices are discrete additive subgroups of the n-dimensional Euclidean space and have been used in coding for reliability and security in transmissions through different channels. Currently Lattice based cryptography is one of the main subareas of the so called Post-quantum Cryptography. Information Geometry is devoted to the study of statistical manifolds of probability distributions by considering different metrics and divergence measures and have been used in several applications related to data analysis. We will approach here particularly the space of multivariate normal distributions with the Fisher metric and some applications. Some References: - S. Amari, Information Geometry and Its Applications. Springer, 2016. - S. I. R. Costa et al, “Lattices Applied to Coding for Reliable and Secure Communications” Springer, 2017 - S. I. R. Costa, S. A. Santos, J. A . Strapasson, Fisher information distance: A geometrical reading” Discrete Applied Mathematics, 197, 59-69 (2015) - J. Pinele , J. Strapasson, S. I. R. Costa, The Fisher–Rao Distance between Multivariate between Multivariate Normal Distributions: Special Cases, Bounds and Applications, Entropy 2020, 22, 404