Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

The background method is a widely used technique to bound mean properties of turbulent
flows rigorously. This work reviews recent advances in the theoretical formulation and …

In this paper, we consider the Koopman operator associated with the discrete and the
continuous-time random dynamical system (RDS). We provide results that characterize the …

A bstract In this work we report on a new bootstrap method for quantum mechanical
problems that closely mirrors the setup from conformal field theory (CFT). We use the …

We present methods for bounding infinite-time averages in dynamical systems governed by
nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov …

For any quantity of interest in a system governed by ordinary differential equations, it is
natural to seek the largest (or smallest) long-time average among solution trajectories, as …

A bstract Bootstrap is an idea that imposing consistency conditions on a physical system
may lead to rigorous and nontrivial statements about its physical observables. In this work …

We study a convex optimization framework for bounding extreme events in nonlinear
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …

We describe methods for proving bounds on infinite-time averages in differential dynamical
systems. The methods rely on the construction of nonnegative polynomials with certain …

The Moment-SOS hierarchy, first introduced in optimization in 2000, is based on the theory
of the S-moment problem and its dual counterpart: polynomials that are positive on S. It turns …