Logarithms and deformation quantization | Vidéo | Carmin.tv

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Logarithms and deformation quantization

By Anton Alekseev

Appears in collection : Braids and arithmetics / Tresses et arithmetique

We prove the statement$/$conjecture of M. Kontsevich on the existence of the logarithmic formality morphism $\mathcal{U}^{log}$. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r = 0$ in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at the boundary which implies the formality property of $\mathcal{U}^{log}$. We also show that the logarithmic formality morphism admits a globalization from $\mathbb{R}^{d}$ to an arbitrary smooth manifold.

Information about the video

Date of recording 14/10/2014
Date of publication 29/10/2014
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18612703
Cite this video ALEKSEEV, Anton (14/10/2014). Logarithms and deformation quantization. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18612703
URL https://dx.doi.org/10.24350/CIRM.V.18612703

Domain(s)

Quantum Algebra

Bibliography

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