Quantum Geometry from Matrices: Framework and Applications

I will discuss the general framework of matrix geometry, which is a version of quantum geometry defined by a set of almost-commuting matrices. This framework allows for an efficient description of manifolds embedded in some target or feature space, which is particularly efficient for high-dimensional manifolds. I will discuss some applications in data science as well as in fundamental physics, notably how spacetime and gravity can emerge from the IKKT or IIB matrix model in this framework.