In 2013, Cachazo, He and Yuan discovered a remarkable framework for scattering amplitudes in Quantum Field Theory (QFT) which mixes the real, complex and tropical geometry associated to the moduli space of n points on the projective line, $M_{0,n}$. By duality, this moduli space has a twin moduli space of $n$ generic points in $P^{n-3}$, leading to dual realization of scattering amplitudes, using a generalization of the CHY formalism introduced in 2019 by Cachazo, Early, Guevara and Mizera (CEGM). Any duality begs for an explanation! And, what physical phenomena lie between the twin moduli spaces? CEGM developed a framework to answer the question for moduli spaces of $n$ points in any $P^{k-1}$, leading to the discovery of rich, recursive structures and novel behaviors which portend an extension of QFT. We discuss recent joint works with Cachazo and Zhang, and with Geiger, Panizzut, Sturmfels, Yun, in which we dig deeper into some of the many mysteries which arise.
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Zoom link: https://pitp.zoom.us/j/95706337178?pwd=cnBka3lFWDBoRlFZV1VadXdGZ1JnZz09