Speaker
Description
Curvature, as captured by the Riemann curvature tensor, is a key notion in (pseudo-)Riemannian geometry and General Relativity. Nonperturbative quantum gravity, formulated in terms of more general, "random" metric spaces, like causal dynamical triangulations (CDT), forces us to take a new perspective on curvature. Because of the intrinsic coordinate invariance of such approaches, this perspective may in some sense be more physical than that of standard GR textbook folklore, but at the same time raises interesting questions. Do meaningful notions of curvature exist in a highly nonclassical regime? What is more elementary, "the metric" (lengths and angles) or "curvature"? In the absence of tensor calculus, can we capture directional aspects of curvature? How does curvature behave under a change of scale? -- I will summarize some insights that have been gained so far by studying the new Quantum Ricci Curvature in the context DT and CDT quantum gravity.
