Information Geometry

Nihat Ay studied mathematics and physics at the Ruhr University Bochum and received his Ph.D. in mathematics from the University of Leipzig in 2001. He was a Postdoc at the Santa Fe Institute and at the Redwood Center for Theoretical Neuroscience, UC Berkeley.  Since 2005, he is Group Leader at the Max Planck Institute for Mathematics in the Sciences in Leipzig, heading the Information Theory of Cognitive Systems group. He works on information geometry, complexity and information theory, mathematical learning theory, embodied cognitive systems, graphical models and causality, and robustness theory. Nihat Ay is Professor of the Santa Fe Institute and Honorary Professor for Information Geometry at the University of Leipzig.  Jürgen Jost studied mathematics, physics, economics and philosophy in Bonn 1975-1980. PhD in Mathematics in 1980, Postdoc at IAS Princeton, UC San Diego, CMA Canberra and Bonn, Professor at Ruhr University Bochum 1984-1996, Director Max Planck Institute for Mathematics in the Sciences, Leipzig, since 1996. Honorary Professor Leipzig University, External Member Santa Fe Institute, Leibniz Award of the DFG 1993, ERC Advanced Grant 2010; works in Riemannian geometry, geometric analysis, dynamical systems, information theory, network analysis, mathematical biology and neurobiology, mathematical economics, complex systems theory. Hông Vân Lê studied mathematics at the Moscow State University and received her Ph.D. in mathematics in 1987 and her DrSc  in mathematics in 1990. She was a Postdoc at the Moscow State University, the International Center for Theoretical Physics (ICTP) in Trieste, the Max Planck Institute for Mathematics in Bonn, a Heisenberg  Fellow at the Max Planck Institute for Mathematics in Bonn, the Henri Poincaré Institute in Paris, the Newton Institute in Cambridge and Leipzig University, a research associate at the Max Planck Institute for Mathematics in the Sciences in Leipzig, foreign Professor at the Abdus Salam School of Mathematics in Lahore, visiting Professor at the Vietnam National University for Sciences in Hanoi. Prize of Moscow Mathematical Society in 1990, Prize of ICTP in 1991, Heisenberg Fellowship of  DFG 1994. Since 2005 she is a senior researcher at the Institute of Mathematics of the Czech Academy of Sciences. She works in Riemannian geometry, symplectic topology, representation theory, differential topology and information geometry.  Lorenz Schwachhöfer studied mathematics and computer science in Darmstadt, New Orleans (Tulane) and Philadelphia (UPenn) where he received his PhD in 1992. He was a Postdoc in St.Louis (Washington Univ.), Bonn (Max Planck Institute for Mathematics) and Leipzig University where he completed his Habilitation in 1998. He was Professor (Chargé de cours) at ULB Brussels (2000-2003), since 2003 he is Full Professor at TU Dortmund University. In 2010, he received the E. Catalan prize of the Royal Academy of Science (Belgium). His main research interests are in differential geometry and differential topology, representation theory and information geometry.

1 Introduction.- 2 Finite information geometry.- 3 Parametrized measure models.- 4 The intrinsic geometry of statistical models.- 5 Information geometry and statistics.- 6 Application fields of information geometry.- 7 Appendix.

"The monograph is very timely and welcome. It will become a standard textbook and reference for the field. It is not only accessible and useful for scientists who work in probability or statistics, but also for all graduate students of mathematics." (Andreas Knauf, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 121, 2019)
"This book also provides a general framework that integrates the differential geometry into the functional analysis, it is an easy read for graduate students in mathematical statistics. I believe that it could be standard reference for information geometry." (Etsuo Kumagai Hamada, Mathematical Reviews, June, 2018)

"The book as well as [Shun-ichi Amari's Information Geometry and its Applications] will remain standard textbooks on information geometry in the foreseeable future and will become the classics in the arena afterwards." (Hirokazu Nishimura, zbMATH 1383.53002)