Probability and analysis informal seminar
There exists several ways to discretize holomorphic functions. One of them is based on Schramm's orthogonal circle patterns, and their generalization to so-called "cross-ratio maps" and "P-nets". These systems are naturally associated with a discrete time dynamics. I will mention results and open problems about this dynamics, in particular the "Devron" property, that states that singularities cannot be escaped by reversing time. I will show that these questions can be tackled by identifying those (birational) dynamics with the dSKP equation, which itself can be identified with partition functions of (oriented) dimers, a famously integrable model of statistical mechanics. Based on joint works with Niklas Affolter, Béatrice de Tilière, Jean-Baptiste Stiegler.
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Thierry Bodineau, Pieter Lammers, Yilin Wang
