Thomas Rot receives a grant of the NWO Open Competition

How do you remove the air from an inflated balloon? You won’t succeed if you are not allowed to puncture a hole or untie the knot. This phenomenon is mathematically described by a non-trivial homotopy group, which is part of homotopy theory. In this project the homotopy theory of infinite dimensional spaces will be developed. Infinite dimensional spaces might sound exotic, but are fundamental in many models in the sciences. For example the distribution of heat in a metal bar or the spread of an infectious disease are both modeled by equations on infinite dimensional spaces. In such applications the equations themselves are typically not exactly known: Models always simplify the situation, and even if the model would be fully correct, modeling parameters and initial conditions cannot be measured with infinite precision. For applications it is therefore important to understand those properties of the solutions that are robust under perturbations of the equations. The homotopy theory that will be developed in this project is geared to understand these robust properties.