Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples

Quantum Statistical Mechanics of the Absolute Galois Group

“…There is also a product operation on dessins induced by the fibered product of the Belyi maps. It was discussed in [52]. Let D 1 and D 2 be two dessins with f i : X i → P 1 (C) the associated Belyi maps.…”

Adinkras from ordered quartets of BC4 Coxeter group elements and regarding another Gadget’s 1,358,954,496 matrix elements

“…Our study of "Garden Algebras" [1,2] and "adinkras" [3] has opened multiple pathways for understanding the relation of supersymmetry, in most unexpected ways, to topics in mathematics. Such a demonstration appeared in the recent examples [4,5] connecting adinkras to algebraic geometry as the latest following a host of others [6,7,8,9,10,11,12,13].…”

Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget

“…For example, the concept of "the root superfield" [9] has found applications such as the construction of new models and the classification of N-extended supersymmetric quantum mechanical systems in the research of [10,11,12,13,14,15,16]. The program has also created links to purely mathematical discussions such as combinatorics [17], Coxeter Groups [18], and Klein's Vierergruppe [19], and spectral geometry [20]. The adinkra concept has generated at least one publication purely in the mathematical literature [21] and uncovered other surprising structures [22,23].…”