Isaac Pliskin (UMass Math&Physics): General Relativity, Generalized Elasticity, and Torsion

It is well-know that an inspiration for the development Cartan's concept of generalized spaces was Einstein's theory of General Relativity describing gravity as the curvature of spacetime. Less well-known is the second context Cartan had in mind: the generalized theory of elasticity developed by the Cosserat brothers. Cartan's study of the geometrical structures forming the foundations for both theories led to a generalization of the notion of curvature given by two parts; a rotational component which corresponded to the curvature known from Riemannian geometry, and a translational component which seemed to naturally be described by a rotational quantity. The translational curvature was named torsion by Cartan. This talk will aim to give an overview of Cartan's picture of torsion inspired by both General Relativity and generalized elasticity, and to (hopefully) answer the question of why Cartan sought to describe the translational curvature by a rotational quantity.