Abstract:  Gradient-flow dynamics in abstract spaces have attracted increasing attention in the last decades, especially in connection with Wasserstein metrics. In absence of a linear structure, dissipative evolutions of gradient-descent type are usually reformulated in variational terms. Generalized minimizing movements and evolution variational inequalities are two important concepts arising in this context. The starting point for both concepts is to specify the cost of evolving between two distinct states of the system. A quite complete theory is currently available for costs being the power of the distance in a complete metric space. In this lecture, I aim at presenting some first results for the case of more general costs, eventually leaving the metric-space setting. In particular, I will present an existence theory of evolution variational inequalities. This is work in collaboration with Pierre-Cyril Aubin-Frankowski (TU Wien) and Giacomo Enrico Sodini (University of Vienna).

For further information please contact elisur.magrini@unibocconi.it.