Plane quartics and heptagons

In a recent paper with Kathlén Kohn, Ragni Piene, Kristian Ranestad, Felix Rydell, Boris Shapiro, Miruna-Stefana Sorea, and Simon Telen, we conjectured, based on numerical computation, that a general quartic plane curve is the adjoint of 864 heptagons in the plane. The adjoint curve of a polygon is the numerator of its canonical function appearing in the context of positive geometry. The goal of the talk is to explain the context of this result and give a proof of this number via intersection theory. This is joint work with Daniele Agostini, Daniel Plaumann, and Jannik Wesner.