# Research

The central object of my research is the Generalized Moment Problem (GMP) as it is discussed in Lasserre: Moments, Positive Polynomials and Their Applications. Investigating both, the primal and the dual formulation of the GMP, I am working in the intersection of functional analysis and real algebraic geometry. Applications of the GMP are numerous and diverse, e.g, when imposing polynomial data, problems of *Global Optimization*, *Differential Equations*, and *Probability Theory* can be approached.

I am working on both facets of the GMP and neighbouring fields, e.g. *Certificates of Positivity *and *Calculus of Variations*. As applications I am currently interested in *Optimal Control of Partial Differential Equations* and *Stochastic Optimization.*

For reasons of scalability I am particullarly interested in how *Sparsity *can be exploited in different applications using the GMP approach.