Matrix models and convex polyhedra

I will tell about the application of the matrix-model approach to the description of convex integer polyhedra and toric geometry associated with them. There are many examples of matrix models that describe various invariants of geometric objects: Hurwitz numbers, intersection numbers on module spaces, etc. The connection goes through the combinatorics of these invariants and the diagram technique of the corresponding models. Toric geometry is reformulated in terms of convex integer polyhedra, so we try to apply the technique of matrix models in this case as well. I will tell: - how it is possible to construct a similar model listing two natural (in the context of toric geometry) combinatorial characteristics of polyhedra: the number of internal integer points and subsections - how do these combinatorial objects arise in Batyrev's theory of mirror-symmetric Calabi-Yau hypersurfaces - how are the Ward identities and Virasoro-like algebra, which arise in this model, arranged