Superlinear structures, or more precisely symmetric monoidal tensor structures, implicitly appeared in mathematics and physics long time ago, among others having roots dating back to Graßmann calculus in mathematics and the study of Fermi statistics and the Dirac exclusion principle in physics, later emphasised in supergravity and string theory.
On the other hand, conformal geometry also dates back to the 19th century. It emerged in physics through the study of conformal invariant theories. Seeking unified structures in regard of the Coleman-Mandula no-go-theorem, this was brought together with supersymmetry and lead to the concepts of superconformal symmetry groups and superconformal field theories.
In this lecture we first give an overview of the underlying basic mathematical notions of superlinearity and conformal geometry. Then we draw some mathematical conclusions, mainly from a representation theoretic perspective. Finally we discuss certain results from representation theory, that could be possibly relevant for some new relationship between the standard model and superconformal field theories.