报告题目：Dissipative Measure Differential Equations: Explicit and Implicit Euler schemes

报告人：Giulia Cavagnari研究员 意大利米兰理工大学

时间：2024年11月11日 14:30

地点：数学楼2-2会议室

报告摘要： We present an overview on the study of well-posedness for Measure Differential Equations. These are first order evolution equations of probability measures on the Wasserstein metric space, driven by probability vector fields. Existence and uniqueness of solutions can be addresses by mimicking the classical theory of dissipative evolutions in Hilbert spaces and employing explicit or implicit Euler schemes. To this end, we need to study an appropriate notion of dissipative operator in our measure-theoretic framework, whose key examples are the gradient of (geodesically) convex functionals. We then discuss an approach based on an Explicit Euler method and another approach based on an Implicit Euler method. This last one is performed in the lifted space of random variables parametrizing the probability measures involved in our evolution.

This is a joint work with Giuseppe Savaré (Bocconi University - Italy) and Giacomo Enrico Sodini (University of Vienna - Austria).

报告人简介：Giulia Cavagnari is a researcher in Mathematical Analysis at Politecnico di Milano (Italy).

She got her PhD in 2016 at Universities of Trento and Verona (Italy) and she held a total of three years postdocs: one year at Rutgers University-Camden (USA),  two years at the University of Pavia (Italy).

She has been invited to several national and international conferences or short research periods abroad. She is currently spending a teaching period at the iHarbour campus of XJTU in Xi'an for the XJTU-PoliMI Joint School in Design and Innovation (17 September-15 November 2024).

The research interests of Giulia Cavagnari lie at the interface between Optimal Transport, Optimal Control, Set-valued analysis and Monotone evolutions. In particular, her research contributions regard the study of optimal control problems in the Wasserstein space of probability measures (with applications to multi-agent systems) and, more recently, the study of dissipative/anti-monotone evolutions in Wasserstein spaces.