Many changes have happened in my life recently!
I defended my doctorate on November 17th. I guess I’m a doctor now! There are too many people to thank for that, so please see the “Thanks” section of my thesis. I am now entering the scary world of job applications. I am discovering the wonderful “GALAXIE” web application – fellow French job applicants know my pain.
Fortunately, starting on February 1st, I have had the chance of becoming a postdoc at ETH Zürich in the group of Thomas Willwacher, funded by his ERC grant 678156–GRAPHCPX. So for the next two years (and perhaps even a third) the pressure of job applications will hopefully not weigh down too much.
Between all these administrative troubles I am still doing math, of course. With Ricardo Campos, Pascal Lambrechts, and Thomas Willwacher, we have uploaded a preprint of our work on configuration spaces of manifolds with boundary, a follow-up to my previous paper and the paper of Ricardo and Thomas. Our paper paper contains the third chapter of my thesis (which I had done in collaboration with Pascal), as well as several new results and ideas.
With 107 pages, our paper contains many new results. Most prominently, we prove that the real homotopy types of configuration spaces of manifolds with boundary only depends on the real homotopy type of the pair (manifold, boundary), provided the manifold and its boundary are simply connected and the dimension of the manifold is at least 4. Obviously, operads are involved, and the models we obtain are compatible with the action of the little disks operads and/or the Swiss-Cheese operads (more specifically, the Fulton–MacPherson versions of these operads). Moreover, we also have models of configuration spaces which are compatible with “gluing” in some sense, and we plan to use these results to obtain models of configuration spaces of manifolds that can be written as unions of submanifolds. Stay tuned!