Limits of geometries over the p-adic numbers

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 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. Those are central in number theory, algebraic geometry, representation theory. The grant will fund one PhD student and one postdoc.