Infinite-dimensional Geometry and Artificial Intelligence

In this talk, we will present some applications of finite-dimensional and infinite-dimensional geometry to Artificial Intelligence. The growing need to process geometric data such as curves, surfaces or fibered structures in a resolution-independent way that is invariant to shape-preserving transformations gives rise to mathematical questions both in pure and applied differential geometry, but also in numerical analysis. To illustrate this, applications of shape analysis in medical imaging and temporal alignement of signals will be given. On the other hand, the extraction of geometric information from point clouds formed by data sets is an area where differential geometry meets probability, as in dimension reduction or manifold learning. Some of the challenges in these areas will be mentioned.