Structure and Homotopy of Configuration Spaces (SHoCoS)

December 1st, 2022 – November 30th, 2027


This is a project of fundamental research in mathematics, specifically, algebraic topology, homotopical algebra, and quantum algebra. It is concerned with configuration spaces, which consist in finite sequences of pairwise distinct points in a manifold. Over the past couple of decades, strides have been made in the study and computation of the homotopy types of configuration spaces, i.e., their shape up to continuous deformation. These advances were possible thanks to the rich structure of configuration spaces, which comes from the theory of operads. Moreover, a new theory, factorization homology, allowed the use of configuration spaces to compute topological field theories, topological invariants of manifolds inspired by physics. Our purpose is to exploit the full operadic structure of configuration spaces to obtain new kinds of stabilizations in the homotopy types of configuration spaces, and to use this stability to effectively compute topological field theories from deformation quantization.

This project funded by the Agence Nationale de la Recherche (ANR) under the identifier ANR-22-CE40-0008. It is hosted at Université Paris Cité and it is managed by the CNRS at the IMJ-PRG. The overall budget of the project is 214 k€.


Photo Name Institution
Adrien Brochier Adrien Brochier Université Paris Cité & IMJ-PRG
Yves Guiraud Yves Guiraud INRIA & IMJ-PRG
Najib Idrissi Najib Idrissi (coordinator) Université Paris Cité & IMJ-PRG
Christine Vespa Christine Vespa Aix-Marseille Université & I2M


Postdoctoral position

One postdoctoral researcher position, funded by the SHoCoS project and lasting two years (24 months), will be offered. Applications will open on November 8th, 2023 and close on November 29th, 2023. For more information, please go to the following adress:


See the complete list on the HAL-ANR portal.

  1. Najib Idrissi, Eugene Rabinovich: Homotopy Prefactorization Algebras. Preprint (2023). arXiv:2304.13011. hal-04082483.
  2. Najib Idrissi, Renato Vasconcellos Vieira: Non-formality of Voronov’s Swiss-Cheese operads. Preprint (2023). arXiv:2303.16979. hal-04053257.