Knots and their groups are a traditional topic of geometric topology. In this talk, I will explain how aspects of the subject can be approached as a homotopy theorist, rephrasing old results and leading to new ones. Part of this reports on joint work with Tyler Lawson.

 A central task in modeling, which has to be performed each day in banks and financial institutions, is to calibrate models to market and historical data. So far the choice which models should be used was not only driven by their capacity of capturing empirically the observed market features well, but rather by computational tractability considerations. Due to recent work in the context of machine learning, this notion of tractability has changed significantly. In this work, we show how a neural network approach can be applied to the calibration of (multivariate) local stochastic volatility models. We will see how an efficient calibration is possible without the need of interpolation methods for the financial data. Joint work with Christa Cuchiero and Josef Teichmann.