Recent Results on Information Geometry

C.T.J. Dodson, School of Mathematics. Manchester University.

Luns 14, mércores 16 e xoves 17 de febreiro de 2005 ás 12 horas no salón de graos.

We introduce first some of the background ideas on information theory and its role in studying analytic models for stochastic processes and the geometrization of families of measure functions. This is then used to present the geometry of important examples of the Riemannian manifolds that arise. Next, we obtain the proof of two theorems that characterise the metric neighbourhoods of the two distinguished fundamental states: randomness and independence. These methods have had applications in modelling cryptographic attacks, cosmological void distributions, porous media, clustering of galaxies, communications, and amino acids along protein chains in genomes.

© María Elena Vázquez Abal.