p-Adic Invariants in Algebraic Geometry

Many problems in the sciences can be recast as, or approximated by, seeking solutions to polynomial equations. The goal of this project is to get new insights into the solutions to such equations, using methods from geometry. More specifically, we will use so-called p-adic invariants, which are derived from fractal-like number systems based on a chosen prime p, connecting number theory and geometry. We propose to exploit recent progress in the field to study new properties of these p-adic invariants, give refinements which should capture more information, and use them to analyze geometric objects arising as solutions to polynomial equations. On a structural level, the grant would be used to build up a new research group in the internationally important area of algebraic geometry at the University of Copenhagen, and to recruit two PhD students and two postdocs.