Six balloons tied together in a bunch arrange themselves in an octahedral fashion. As balloons are popped the resulting number conforms to the molecular shapes of VSEPR theory. To Conduct ...

Semigroups, algebraic structures defined by a set equipped with an associative binary operation, are a cornerstone within modern algebra. Their study encompasses both abstract theoretical development ...

Algebraic structures such as operads, Lie algebras and higher A∞-algebras underpin many foundational aspects of modern mathematics. When combined with homotopy theory—the study of continuous ...