Sebastián Tapia (IMB) : « Self-contracted dynamics and extensions. »
Self-contracted dynamics were introduced in 2010. This is a metric property which is an abstract framework for several dynamics that come from optimization. The rectifiability of self-contracted curves was the main question about this phenomena, which was established in 2015 for finite dimensional Euclidean spaces and in 2017 for finite dimensional normed spaces. In this talk we present some results concerning self-contracted dynamics, the main ideas of the euclidean technique for rectifiability and we explore different extensions of the self-contracted notion.