Title: The shape of relations: games, knots and other stories

Abstract: Literature Nobel prize winner A. Solzhenitsyn wrote: "Topology! The stratosphere of human thought! In the XXIV century it might just possibly be of use to somebody, ...".  Developed in the XXI century,  Topological Data Analysis (TDA) offers powerful methods for uncovering patterns in complex datasets by analyzing their shape. In this talk, we will explore tools for visualizing high-dimensional maps and detecting relations between data sets with expected correlations. We will demonstrate the utility of these tools with real-world examples from game theory and cancer genomics, as well as from theoretical mathematics: knots and their invariants.