Infinite Dimensional Riemannian Geometry and Geometric Data Science

Explore a one-hour lecture that delves into the intersection of infinite dimensional Riemannian geometry and modern data science applications, delivered at the Erwin Schrödinger International Institute's Thematic Programme. Learn how recent advances in imaging technologies have sparked new mathematical approaches in biomedical imaging, neuroscience, and medicine, leading to the development of geometric shape analysis and topological data analysis. Gain insights into the fundamental concepts of infinite dimensional Riemannian geometry and understand its unique phenomena. Examine Sobolev metrics on spaces of curves and surfaces, including their geodesic equations' local and global well-posedness and geodesic distance properties. Discover practical applications through the exploration of numerical implementations of statistical frameworks based on these geometric concepts.