Oberseminar "Mathematische Logik" - Dr. Nicholas Pischke

On the surface, the theory of probability measures requires the use of proof theoretically strong principles to already develop some of the most basic notions. Contrary to these apparent limitations, an approach for extending the program of proof mining to this area has recently been proposed. This approach, which is fundamentally based on the use of probability contents (i.e., finitely additive [0,1]-valued functions defined on algebras of sets), has proven to be widely effective based on a range of new case studies presented in the last year. In this talk, we give a short overview of both the theoretical work that supports this endeavor, as well as recent applications to stochastic analysis and optimization which rely on these methods. The talk is based on various (joint) works, in collaboration with Morenikeji Neri, Paulo Oliva and Thomas Powell.