During his PhD studies, Emil Dare researched new mathematical formulae in the field of integral geometry. This branch of mathematics provides tools to deduce the shape and properties of objects by studying lower-dimensional slices of them. Imagine trying to understand a three-dimensional biological cell by only looking at two-dimensional microscope images – the challenge is to connect the local information from slices to the global structure.

In his research, Emil Dare developed new versions of classical formulae that make it possible to calculate not only basic properties such as volume and surface area, but also more refined features like orientation. These results extend existing theory and are useful in practical settings where randomness is limited. The methods have applications in stereology, materials science, and biological imaging.

The new findings strengthen the mathematical foundations for turning partial observations into reliable knowledge about complex structures.

The PhD study was completed at the Department of Mathematics, Faculty of Natural Sciences, Aarhus University.

This summary was prepared by the PhD student.

Time: 10 November 2025 at 12:15
Place: Building 1532, room 116, Lecture Theatre G1, Department of Mathematics, Ny Munkegade 118, Aarhus University, 8000 Aarhus C.
Title of PhD thesis: Crofton and Blaschke–Petkantschin Formulae: Applications in Stereology and Intersection Probabilities
Contact information: Emil Dare e-mail: dare@math.au.dk, tel.: +45 28294720
Members of the assessment committee:
Associate Professor Anne Marie Svane, Department of Mathematics, Aalborg University, Denmark
Professor Matthias Reitzner, Department of Mathematics, Osnabrück University, Germany
Professor Peter Jørgensen (chair), Department of Mathematics, Aarhus University, Denmark
Main supervisor: Associate Professor Markus Kiderlen, Department of Mathematics, Aarhus University, Denmark
Co-supervisor: Associate Professor Claudia Strauch, Department of Mathematics, Aarhus University, Denmark
Language: The PhD dissertation will be defended in English

The defence is public.
The PhD thesis is available for reading at the Graduate School of Natural Sciences/GSNS, Ny Munkegade 120, building 1521, 8000 Aarhus C