Arne Lien from Universität Konstanz had the first part of seocondment with Centre Inria d’Universitè Côte d’Azur from 04.04.2022-02.05.2022.
In this secondment, Arne was looking into a project where the goal is to give a (simpler) semialgebraic description of the image of nonnegative ternary quartics under a certain mapping of rational invariants. Inequalities describing this image is already known, but they involve a few "dummy" variables that we would like to eliminate. Thus the purpose of the project is to find a way to achieve this goal.
The first part of the secondment was spent on understanding the set up for the problem and to consider a simplified version of the problem. So instead of considering the three variable case, I looked at the same question for the two variable case. Then Arne tried exploiting some symmetries in the problem to see if this could be of any use and started looking into the topic of "Cylindrical Decomposition" to see if this process could be amended to work in this scenario. This investigation is not complete however and so he will continue looking into this idea in the last part of the secondment.
The first part of the secondment was also used to discuss the (main) project Arne is working on in Konstanz and also to learn about Tobias Metzlaff’s and Sebastian Debus’ projects who are working on related topics.
Inria d’Universitè Côte d’Azur