edited by Ole E Barndorff-Nielsen (University of Aarhus, Denmark) & Eva B Vedel Jensen (University of Aarhus, Denmark)

This proceedings volume focusses on the applications of geometry in present day science. It contains contributions from a variety of fields, including biology, computer science, mathematics, medicine, physics and stochastics.

• Quantum Geometry (J Ambjørn)
• Extending the Fisher Metric to Density Matrices (D Petz & Cs Sudár)
• Geometry of Quantum Information Systems (A Fujiwara)
• Information Geometric Analysis of an Interior Point Method for Semidefinite Programming (A Ohara)
• Diffusion Processes, Manifolds of Exponential Densities, and Nonlinear Filtering (D Brigo)
• From Computerized to Geometric and Discrete Topography (R J Gardner)
• The Use of the Generalized Blaschke–Petkantschin Formula in Local Stereology and Its Proof by Induction (E B V Jensen & J Nielsen)
• The Stereological Estimation of the Euler–Poincaré Characteristic Exemplified with Networks of Capillaries and Cancellous Bone (J R Nyengaard & H J G Gundersen)
• Geometry, Statistics, and Shape (W S Kendall)
• Solutions to Nonlinear Partial Differential Equations: A Geometric Approach (S D Peckham)
• Voronoi Diagrams and Morse Theory of the Distance Function (D Siersma)