Equivariant formality and reduction | Vidéo | Carmin.tv

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Equivariant formality and reduction

By Chiara Esposito

Appears in collection : Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie Supérieures

In this talk, we discuss the reduction-quantization diagram in terms of formality. First, we propose a reduction scheme for multivector fields and multidifferential operators, phrased in terms of L-infinity morphisms. This requires the introduction of equivariant multivector fields and equivariant multidifferential operator complexes, which encode the information of the Hamiltonian action, i.e., a G-invariant Poisson structure allowing for a momentum map. As a second step, we discuss an equivariant version of the formality theorem, conjecturedby Tsygan and recently solved in a joint work with Nest, Schnitzer, and Tsygan. This result has immediate consequences in deformation quantization, since it allows for obtaining a quantum moment map from a classical momentum map with respect to a G-invariant Poisson structure.

Information about the video

Date of recording 09/05/2024
Date of publication 29/05/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20173903
Cite this video Esposito, Chiara (09/05/2024). Equivariant formality and reduction. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20173903
URL https://dx.doi.org/10.24350/CIRM.V.20173903

Domain(s)

Quantum Algebra

Bibliography

ESPOSITO, Chiara, KRAFT, Andreas, et SCHNITZER, Jonas. The strong homotopy structure of BRST reduction. Pacific Journal of Mathematics, 2023, vol. 325, no 1, p. 47-83. - https://doi.org/10.2140/pjm.2023.325.47
ESPOSITO, Chiara, KRAFT, Andreas, et SCHNITZER, Jonas. The strong homotopy structure of Poisson reduction. Journal of Noncommutative Geometry, 2022, vol. 16, no 3. - https://doi.org/10.4171/JNCG/455

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