Francesco Mori (LPTMS)
Stochastic resetting: from geometric properties to optimal control
"When in a difficult situation, it is sometimes better to give up and start all over again''. While this empirical truth has been regularly observed in a wide range of circumstances, quantifying the effectiveness of such a heuristic strategy remains an open challenge. In this talk, I will first consider the minimal model of a single diffusive particle that is reset to its starting position with a constant rate. I will present recent results on the geometrical properties of this process, including the convex hull  and the number of visited sites . Then, I will introduce a novel framework that allows to optimally control a very general class of dynamical systems through restarts . This approach, analog to the celebrated Hamilton-Jacobi-Bellman equation, is successfully applied to simple settings and provides the basis to investigate realistic restarting strategies across disciplines.
 S. N., Majumdar, F. Mori, H. Schawe, and G. Schehr, Phys. Rev. E 103, 022135 (2021).
 M. Biroli, F. Mori, and S. N. Majumdar, preprint arXiv:2202.04906 (2022).
 B. De Bruyne and F. Mori, preprint arXiv:2112.11416 (2021).