Mateusz Piorkowski: Algebraic equations for arctic curves of the periodic Aztec diamond

Abstract:

In this talk I discuss arctic curves of the kxl-periodic Aztec diamond recently studied by Berggren & Borodin ’23 (arXiv:2306.07482). Polynomial equations for these arctic curves are obtained using theta function of the associated spectral curve. As a corollary we determine the degree of arctic curves in terms of the number of smooth and frozen regions of the underlying model.

The key to this result is a generalization of the classical discriminant of a polynomial to the setting of meromorphic sections on compact Riemann surfaces.