When two entities, like epidemics, business brands or opinions, evolve in competition for space, can they occupy large parts of the available space simultaneously, or will one of them outcompete the other?

One of the most important avenues of research in mathematical physics evolves around a differential equation, introduced by physicists Kardar, Parisi and Zhang. This equation has in empirical studies been found to describe the evolution, over time, of the front of various spatial growth processes, such as bacteria colonies and flame fronts.

The aim of the project is to examine and understand certain spaces of polynomials in many variables.

This is a project in algebraic geometry, the branch of mathematics which studies geometric objects arising from algebraic ones, such as solutions of polynomial equations. The proposal revolves around a central theme within algebraic geometry: the classification problem.

The aim of this project is to establish inequalities between eigenvalues in different physical constellations, focusing on eigenvalues of Laplace and Schrödinger differential equations.

This is a project in algebraic geometry, the branch of mathematics which is concerned with the study of geometric objects that can be described through polynomial equations. These are called (algebraic) varieties.