Аннотация:
The report will focus on the Zamolodchikov tetrahedron equation, which is the next n-simplex equation after the Yang-Baxter one. I will talk about the most striking embodiments of this equation in my opinion: namely, its role in the theory of cluster varieties, the theory of 2-knot invariants, that is, classes of isotopes of embeddings of a two-dimensional surface into a 4-dimensional space, exactly solvable models of statistical physics in dimension 3 and integrable quantum mechanical models on two-dimensional lattices.