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"Polytope algebra" by Gaiane Panina

We will gradually build up a beautiful algebraic object based on purely geometric objects — the polytope (graded) algebra developed by Peter McMulen. That is, we will introduce addition, multiplication, and even such crazy things as exponent and logarithm for polytopes. This construction has helped to prove the f-vector problem (I’ll try to hint how) and is directly related to the Chow rings of algebraic toric varieties (this is beyond our course). Surprisingly, there are no prerequisites. However, it is nice if you know what an abelian (that is, commutative) group, a ring, and the (graded) algebra of polynomials are.

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