In this talk we discuss structure preservation and deep learning for classifying, analysing and manipulating shapes. A computationally demanding task for estimating distances between shapes, e.g. in object recognition, is the computation of optimal reparametrizations. This is an optimisation problem on the infinite dimensional group of orientation preserving diffeomorphisms. We approximate diffeomorphisms with neural networks.

We will discuss useful geometric properties in this context e.g. properties of the distance function, and inherent geometric structure of the data. 

Another interesting set of related problems arises when learning dynamical systems from (human motion) data.

Refreshments will be served preceding the talk, starting at 2:45.