Matyroshka dolls and tinkertoys: Calabi-Yau geometry and supersymmetry
The geometry of Calabi-Yau manifolds and supersymmetry are key ingredients in string theory. We will take a non-traditional point of view on both of these. The hereditary structure of nested Calabi-Yau manifolds underlies string dualities and motivates an algebraic reinterpretation. Dimensional reduction of supermultiplets produces a discrete scaffolding (Adinkra graphs) that nevertheless possesses an emergent form of geometry. Surprisingly, we find that supermultiplets themselves bear the stamp of Calabi-Yau geometry. Our proof of this uses work of H.S.M. Coxeter inspired by a woodcut by M.C. Escher. The talk is designed to be broadly accessible to graduate students.