At the root of scientific evolution, classifying all possible geometries of a given object and exploring all possible transitions between them are crucial. Often, geometries are modeled over our usual number system, the real numbers. Instead, my research project will focus on geometries modeled over the $p$-adic numbers, where $p$ is a prime number and the digits used are from $0$ to $p−1$. The objective is to answer the following fundamental questions for many of the possible $p$-adic geometries: Given a family of geometries, can one compute all its possible limits of geometries? Can one provide precise geometric transitions towards those limits? The grant will fund the recipient as well as one PhD and one postdoc.