CE40 - Mathématiques

Structure and Homotopy of Configuration Spaces – SHoCoS

Submission summary

This pre-proposal 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.

Project coordination

Najib Idrissi-Kaïtouni (Institut de mathématiques de Jussieu - Paris Rive Gauche)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


IMJ-PRG Institut de mathématiques de Jussieu - Paris Rive Gauche

Help of the ANR 214,175 euros
Beginning and duration of the scientific project: November 2022 - 60 Months

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