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Symmetry, rigidity and polymatroidal functions

In rigidity theory, we attempt to determine whether physical structures are rigid or flexible using pure mathematics. One of the most commonly used models are bar-and-joint frameworks (G,p), where G is a graph whose edges represent bars of fixed length, and p assigns coordinates to each vertex. Many important results in rigidity theory only apply when the coordinates in p are algebraically independent over the rationals. However, this is not a realistic assumption for real-world structures. In this talk I'll explain how classical methods from rigidity theory have been adapted to analyse symmetric structures.