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AU-MATH

Stochastic geometry group at Department of Mathematics, Aarhus University


The stochastic geometry group comprises presently the following researchers:

  • Rikke Krog Eriksen, PhD student
  • Ute Hahn, associate professor
  • Louis Gammelgaard Jensen, PhD student
  • Eva B. Vedel Jensen, professor
  • Markus Kiderlen, associate professor
  • Andrew du Plessis, associate professor
  • Anders Rønn-Nielsen, associate professor
  • Mads Stehr, PhD student
  • Helene Svane, PhD student

Within CSGB, the AU-math group is engaged in advanced mathematical research as well as in practical applications.

A key research topic for AU-math is tensor valuations in stochastic geometry, including their integral geometry, their role in stochastic modelling and their estimation from digital grey-value images. Tensor valuations may be used as shape descriptors. Methods for estimating shape and orientation of particles from tensor valuations are studied in close collaboration with AU-bio.

Another important research topic for AU-math concerns statistics for stochastic geometry models. In particular, the statistical properties of Monte Carlo envelope tests for functional data are studied.

Competences

  • Stereology
  • Stochastic geometry
  • Topology
  • Statistics for functional data
  • Brain imaging

The AU-math group is located at Department of Mathematics, Aarhus University. The group is recognized world-wide for its research in mathematical stereology. The local stereological methods, developed in collaboration with the AU-bio group, are used as central tools in an unusually wide range of disciplines, including biology, materials science and medicine. Within the last decade, the group has broadened its research focus that now also involves basic research in integral and stochastic geometry, and spatial statistics.

The AU-math group is led by Markus Kiderlen. His main contributions are in convex and integral geometry, geometric tomography, stochastic geometry and stereology. His achievements in geometry encompass the up-to-date strongest stability results in tomography for convex bodies, parallel volume expansions and the solution of Hammer’s X-ray reconstruction problem. In recent years, he has made important contributions to the field of digital geometry. He was one of the three directors of the Danish Council for Strategic Research’s Histoinformatics project in 2007-2010. More information at the homepage of Markus Kiderlen.

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Revised 04.09.2018