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.