Speaker
Description
The search for a theory that consistently combines quantum theory with general relativity forces us to consider geometrical frameworks beyond standard (first order) differential geometry. One candidate for such a generalized geometrical framework is second order (stochastic) differential geometry, which incorporates a violation of Leibniz rule, that is characteristic to the Wiener integral, into the geometry. This feature makes the framework an ideal tool in the study of covariant path integrals.
In this talk, I will review the basic ingredients of this framework in both a Euclidean and Lorentzian signature. I will pay particular attention to the deformations of spacetime symmetries that arise due to the coupling of spacetime fluctuations to the affine connection, and discuss some connections to non-commutative geometry.
