Abstract: To describe quantum gravity via gauge/gravity duality, it is important to understand how geometry on the gravity side emerges from gauge theory degrees of freedom. The simplest scenario is to identify the eigenvalues of matrix-valued fields with spatial coordinates. For a long time, such a scenario was not pursued because Polchinski raised a puzzling issue in 1998. In this talk, we give a simple resolution to the puzzle raised by Polchinski, which enables us to use "eigenvalues = spatial coordinate"-picture to describe the entire bulk geometry. By combining this with recent development on the understanding of the confinement/deconfinement transition, we explain how black hole geometry is encoded into matrix degrees of freedom. If time permits, we will explain how the Page curve follows from this geometric interpretation.