The Kashiwara-Vergne theory and 2-dimensional topology | Vidéo | Carmin.tv

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The Kashiwara-Vergne theory and 2-dimensional topology

By Anton Alekseev

Appears in collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

The Kashiwara-Vergne problem is a property of the Baker-Campbell-Hausdorff series which was designed to study the Duflo Theorem in Lie theory. Surprisingly, it is related to many other fields of Mathematics including the Drinfled’s theory of associators and the theory of multiple zeta values. An interesting new development is a link between the Kashiwara-Vergne theory and 2-dimensional topology encoded in the Goldman bracket and Turaev cobracket on spaces of homotopy classes of loops on surfaces. The talk is based on joint works with B. Enriquez, N. Kawazumi, Y. Kuno, F. Naef, E. Meinrenken and C. Torossian.

Information about the video

Date of recording 07/06/2017
Date of publication 12/06/2017
Institution IHES
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4

Domain(s)

Bibliography

A. Alekseev and F. Naef. Goldman-Turaev formality from the Knizhnik-Zamolodchikov connection. C. R., Math., Acad. Sci. Paris 355, No. 11, 1138--1147 (2017; Zbl 1425.17029) arXiv:1708.03119
A. Alekseev et al. The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem. Adv. Math. 326, 1--53 (2018; Zbl 1422.57053) arXiv:1703.05813
Alekseev, A.; Enriques, B.; Torossian, C., Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations, Publ. Math. Inst. Hautes Études Sci., 112, 1, 143-189 (2010, Zbl 1238.17008) arXiv:0903.4067
Alekseev, A.; Meinrenken, E., On the Kashiwara-Vergne conjecture, Invent. Math., 164, 615-634 (2006, Zbl 1096.22007) arXiv:math/0506499

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