This talk introduces an ongoing research project focused on building mechanistic models to study retinal degeneration, with a particular emphasis on the geometric aspects of the disease progression.

As we develop a computational model for retinal degeneration, we will explore how cellular materials behave and how wound-healing mechanisms influence disease progression. Finally, we’ll detail the numerical methods used to simulate these processes and explain how we work with medical data.

Ongoing research in collaboration with the group of M. Paques (Paris Eye Imaging - Quinze Vingts National Ophthalmology Hospital and Vision Institute).

The goal of the talk is to give an overview of the metric theory of currents by Ambrosio-Kirchheim, together with some recent progress in the setting of Banach spaces. Metric currents are a generalization to the metric setting of classical currents. Classical currents are the natural generalization of oriented submanifolds, as distributions play the same role for functions. We present a structure result for 1-metric currents as superposition of 1-rectifiable sets in Banach spaces, which generalizes a previous result by Schioppa. This is based on an approximation result of metric 1-currents with normal 1-currents. This is joint work with D. Bate, J. Takáč, P. Valentine, and P. Wald (Warwick).