In the coming years, the large amount of data that experiments at the Large Hadron Collider will collect will lead to an unprecedented increase in the precision of their measurements. An important process under high experimental scrutiny is that of the production of a top/anti-top pair in association with a W boson. Precise understanding of this experimental signature will allow us to strongly constrain anomalous electro-weak couplings in the top sector. Nevertheless, measurements of ttW production are already in tension with theoretical predictions. In order to better understand this discrepancy, it is essential that the precision of the theoretical precision match the experimental measurements. Crucially, these predictions require two-loop scattering amplitudes whose computation poses a theoretical challenge due to the analytic complexity of the underlying Feynman integrals. In this project, we will use geometric and mathematical tools to understand the mathematical structures which underpin the amplitudes which will allow us to develop novel approaches to overcome these challenges and compute the two-loop amplitudes for the production of a tt pair in association with a W boson.