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Abstract:  According to the Gaiotto–Moore–Neitzke algorithm, spectral networks associated to differentials on Riemann surfaces can be used to compute the BPS states of certain supersymmetric quantum field theories. The construction of spectral networks associated with cubic differentials admits a particularly simple description in terms of flat geometry: they appear as graphs of straight trajectories that generate new ones upon intersection under certain conditions. We present the notion of spectral core as a refinement of the classical core concept by Haiden, Katzarkov, and Kontsevich in flat surface theory, and show that it precisely controls the birthing process of spectral networks trajectories. As an application, we describe the spectral networks corresponding to polynomial cubic differentials of degree d=3. Time permitting, we will also discuss the problem of characterizing cubic differentials whose associated spectral networks generated by the algorithm have finite complexity. This work is a collaboration with Omar Kidwai.