# Structure and Homotopy of Configuration Spaces (SHoCoS)

December 1st, 2022 – November 30th, 2027

## Presentation

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`

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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€.

## Members

Name | Institution | |
---|---|---|

Adrien Brochier | Université Paris Cité & IMJ-PRG | |

Yves Guiraud | INRIA & IMJ-PRG | |

Najib Idrissi (coordinator) | Université Paris Cité & IMJ-PRG | |

Christine Vespa | Aix-Marseille Université & I2M |

## Events

## Postdoctoral position

More to come later!

## Publications

See the complete list on the HAL-ANR portal.

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