Hosted by: Niklas Mueller

The famous "sign problem" is the main roadblock in the path to a Monte Carlo solution of QCD at finite densities and the study of real time dynamics. We review a recent developed approach to this problem based on deforming the domain of integration of the oath integral into complex field space. After discussing the math involved in the complex analysis of multidimensional spaces we will talk about the advantages/disadvantages of using Lefschetz thimbles, "learnifolds" and "optimized manifolds" as the alternative integration manifold as well as the algorithms that go with them. Several examples of lower dimensional field theories will be presented.