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Fano 3-space and symmetrisation of quad-equations

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Discrete Integrable Systems

Recent results have shown how invariance under interchange of variables and parameters of integrable discrete models can lead to significant generalisation of the domain; giving a more natural lattice geometry that respects the symmetry. I will describe a symmetric generalisation of the polynomials that define the principal rational, trigonometric and elliptic models from the ABS list, namely Q2, Q3 and Q4. They have a property, generalising the consistency on the cube, which involves the finite geometry PG(3,2). This space was discovered originally during investigation of the axiomatic framework for projective geometry by Gino Fano in 1892, and is connected with symmetrisation of the quadrangle.

This talk is part of the Isaac Newton Institute Seminar Series series.

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