Random tensors, from Quantum gravity to Artificial Intelligence

QGB gathers researchers interested in random tensors, a field which generalizes random matrices as a modern tool for scientists. Of particular importance to us are

The combinatorics of Feynman graphs of tensor models which are dual to triangulations of manifolds in arbitrary dimensions. This leads to obvious applications to quantum gravity, much as matrix models and their Feynman graphs are a famous approach to two-dimensional quantum gravity. Indeed, these triangulations of manifolds represent discretized metrics à la Regge. This is the approach which introduced random tensors to combinatorics and physics.

The SYK model which is a candidate for the holographic dual of black holes, and SYK-inspired tensorial field theories. The SYK model and the related tensorial field theories enjoy remarkably interesting properties. In particular, they exhibit conformal invariance and explicit solvability in the infrared and large N limit. Such properties can be understood combinatorially and have made the field one of the most active in theoretical physics in the past few years.

Applications to artificial intelligence. Random tensors are a tool which can generate new results outside its original scope. Random tensors appear naturally in artificial intelligence problem, just as random matrices, e.g. data are stored in the entries of a matrix/tensor but are subjected to noise which has to be negated. We will have a session dedicated to artificial intelligence.