Victor Buchstaber (Steklov Mathematical Institute and University of Manchester)
victor.buchstaber@manchester.ac.uk
Simple polytopes play important role in applications of algebraic geometry to physics. They are also main objects in toric topology.
There is a commutative associative ring P generated by simple polytopes. The ring P possesses a natural derivation d, which comes from the boundary operator. We shall describe a ring homomorphism from the ring P to the ring of polynomials Z[t,α] transforming the operator d to the partial derivative ∂/∂t.
This result opens way to a relation between polytopes and differential equations. As it has turned out, certain important series of polytopes (including some recently discovered) lead to fundamental non-linear differential equations in partial derivatives.