The logic of polyhedra

Duality is a fruitful and time-honoured idea in mathematics. A rational polyhedron is a finite union of  simplexes with rational vertices. Rational polyhedra are dual to finitely presented MV-algebras, i.e., the algebras of formulas in infinite-valued Lukasiewicz logic. Invariant measures on these formulas and their associated rational polyhedra yield the Haar theorem for finitely presented unital abelian lattice-ordered groups, and for a class of finitely presented AF C*-algebras. My talk will be geared towards the non-expert.