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Grants #

My PhD thesis was supported by the ISM and a Excellence Grant (about 2000 euros / 3000 canadian dollars). I was also awarded a Mitacs-Inria Grant (about 4000 euros / 6000 canadian dollars), to support international mobilities.

After having considered symmetric and arbitrary hyperplane arrangements, we are considering extending the methods to the computation of the “subchambers” (the sets that are contained in at least one of the hyperplanes), i.e., computing entirely the arrangement. Clarifying which notions must be adapted (or not!) is important before considering the implementation.
Another possible extension would be the entwinement of the tree algorithm and methods using combinatorial symmetries (for suitable instances, see this and also this).

The analysis of the structure of the minimum C-function yielded a better understanding of a considered globalization technique, and in particular an intriguing complexity estimate of the arising nonsmooth reformulation. Implementing a prototype of the suitable method is a (long-term) goal to verify the relevance of the method.