There have been rapid recent developments in several different research communities in this connection, with little interaction between them, and one of the goals of the conference is to bring these communities in contact.

In statistics, although analysis of the geometric structure of statistical manifolds (i.e., manifolds formed by some families of probability distributions) has its roots in the work of Cramér, Rao and Fisher in the 1940’s, it saw much development in the 1980’s through Amari and others. On the other hand, the algebraic geometry of statistical models began to be studied more recently by Sturmfels and others. The recent development of such algebraic and geometric methods (based on differential geometry or other kinds of geometric structure) has transformed the fields of machine learning and Bayesian statistics.
In physics, the geometric aspects of information theory played an important role in the formalisation and description of quantum states and correlations that are now investigated in the context of quantum gravity.
In probability theory, it is now recognized that information-theoretic inequalities play a foundational role, being closely connected to central themes including limit theorems, concentration of measure, suprema of stochastic processes, convergence rates of Markov processes to stationarity, and so on.
In convex geometry, entropy is closely connected to central questions like the hyperplane conjecture.
In category and homology theory, researchers have advanced on the axiomatization and characterisation of information and probability theory.
In geometry, thanks to work by Lott, Villani and Sturm, entropy has provided new ways of talking about curvature for spaces without a Riemannian structure.

The conference will review many of these new developments, involving the interplay of information and algebraic and differential geometry, number theory, probability and homology. It will emphasize the richness and diversity of information approaches and principles that arose in mathematics, physics, and statistical data analysis. The conference schedule will be organised around half-day and day sessions, covering one central topic. Introductory courses open to students will be proposed at the beginning of the sessions, then completed by more specialized one-hour presentation. Finally, discussion sessions that tackle open questions and future development lines will also take place.

Stéphanie Allassonnière (CMAP X, France)
Marc Arnaudon (IMB, France)
Nihat Ay (Max Planck Institute Leipzig)
Frédéric Barbaresco (Thales Air Systems)
Pierre Baudot (Aix-Marseille Université)
Daniel Bennequin (Université Paris Diderot)
Joël Bensoam (IRCAM Centre Pompidou)
Michel Nguiffo Boyom (Université de Montpellier)
Herbert Gangl (Durham University, UK)
Michel Ledoux (Université de Toulouse)
Mokshay Madiman (University of Delaware)
Mathilde Marcolli (Caltech University)
František Matúš (Academy of Sciences, Czech Rep)
Frank Nielsen (Ecole polytechnique)
Xavier Pennec (Inria Sophia Antipolis)
Carlo Rovelli (CPT, France)
Dominique Spenher (Institut Fourier, France)
John Terilla (Queens College, USA)