The Erwin Schroedinger Institute for Mathematical Physics

Programme: Infinite-Dimensional Riemannian Geometry with Applications to Image Matching and Shape Analysis


January 7 – February 28, 2015

Organisers: Martin Bauer, Martins Bruveris and Peter W. Michor

Special Issue of J. Geom Mech.

We welcome submissions of papers on "Infinite-Dimensional Riemannian Geometry" for publication in a special issue of the Journal of Geometric Mechanics. Submission of papers is by email to the editors. Submission deadline is December 31, 2015.

Editors: Peter W. Michor (associate editor), Martin Bauer and Martins Bruveris (guest editors).

News

  • February 11, 2015. The schedule and abstracts for the week of February 23–27 are now online.
  • January 29, 2015. The schedule and abstracts for the week of February 9–13 are now online.
  • January 23, 2015. The preliminary schedule and abstracts for the workshop on "Riemannnian geometry in shape analysis and computational anatomy", which will take place February 16–20 are now online.
  • January 22, 2015. The schedule and abstracts for the week of February 2–6 are now online.
  • January 21, 2015. The schedule and abstracts for the week of January 26–30 are now online.
  • January 18, 2015. Slides from the first workshop are now online.
  • January 8, 2015. The abstracts for the week of January 19–23 are now online. Please also note the changes in the schedule for the workshop.
  • January 7, 2015. The schedule and abstracts for the workshop on "Infinite-dimensional Riemannian geometry" are now online, as is the schedule of talks for the week of January 19–23.

Workshops

Poster for theoretical workshop The workshop on "Infinite-dimensional Riemannian geometry" will take place January 12–16, 2015. The poster, the schedule and the abstracts of the talks are now online.
Poster for applied workshop The workshop on "Riemannian geometry in shape analysis and computational anatomy" will take place February 16-20, 2015. The poster can be found here.

Lecture courses

In the weeks between the workshops there will be three lecture courses:

  • Peter Michor (Week 2): "Overview on Convenient Calculus and Differential Geometry in Infinite dimensions, with Applications to Diffeomorphism Groups and Shape Spaces" .
  • Gerard Misiolek (Week 4): "Geometry and analysis of the incompressible Euler equations"
  • Xavier Pennec (Week 5): "Geometric Structures for Statistics on Shapes and Deformations in Computational Anatomy"
A short description of the topic of the lecture courses can be found here.

Program Outline

The aim of this programme is to bring together researchers in pure and applied mathematics in order to expand and deepen our understanding of infinite-dimensional manifolds and their Riemannian geometry, with special emphasis on those manifolds, which are used in shape analysis, image matching and computational anatomy.

The manifolds of interest include the spaces of plane and space curves, the space of immersed surfaces and more generally spaces of mappings between finite-dimensional manifolds. A special case, that is interesting in its own right, is the diffeomorphism group, the space of invertible maps of a manifold to itself.

In the field of computational anatomy the diffeomorphism group plays a central role. The space of medical images is acted upon by the diffeomorphism group and differences between images are encoded by diffeomorphisms. The development of robust numerical and statistical methods for analysing medical images is a challenging problem, with geometry being an integral part.