On two different random geometry approaches to quantum gravity

by Carlos Perez (Warsaw University)

Thursday 12 Mar 2020, 14:15 → 16:15 Europe/Berlin

Abbeanum SR 102

Quantum gravity motivates a variety of microscopic models of space and
spacetime. This talk focuses on two of them: On the one hand, on tensor
models, which appeared in the 90's as a simplicial theory of gravity and
more recently regained some interest after Gurau's proof of the
long-sought 1/N-expansion that is analogous to 't Hooft's matrix model
expansion. Some non-perturbative aspects of tensor models will be
discussed and geometrically interpreted. On the other hand, in an
algebraic approach, we address the so-called fuzzy geometries,
originated by spectral truncations of smooth manifolds. These fit into
Connes' spectral formalism of noncommmutative geometry, in which gravity
coupled to matter has a neat (classical) description. After introducing
these concepts, we provide a multi-matrix model description of the
quantization of fuzzy geometries, still without matter. Both frameworks
face common challenges to be discussed.