POEMA Host Institution: LAAS-CNRS, Toulouse, France
Background: I studied inUlm (Germany) and Innsbruck (Austria) and my focus was on functional analysis and dynamical systems
Master thesis: Global attractors and quantitative aspects of dynamical systems via the Koopman semigroup. A functional analytic approach to slow invariant manifolds.
Research interests: Interplay between geometric aspects of dynamical systems and the Koopman semigroup, “linearized” formulations of problems from dynamical systems in terms of occupation measures (e.g. optimal control) and how to solve them.
POEMA project: Polynomial Optimization: Some challenges from applications. One possible direction is to explore and develope different optimization methods for solving infinite dimensional linear programming problems in the space of Borel measures. Traditionally, the Lasserre’s moment sum-of-squares hierarchy is utilized, which yields a sequence of finite dimensional semidefinite programs. However, there are also other methods that could be applied to this class of problems such as those approximating the gradient flow in the space of measures. The second research direction pertains to reinforcing the existing infinite-dimensional LP formulations such as their finite-dimensional approximations exhibit faster convergence. One possible direction is the connections to the spectral theory of the Koopman and Perron-Frobenius operators. Another direction is the exploitation of the Pontryagin maximum principle. Finally nonlinear (optimal) control problems for partial differential equations have been investigated but very general convergence results for Lasserre’smoment-sum-of-squares hierarchy are not known yet.