Online: Seminar, Anton Alekseev (University of Geneva), Conjugation of Words, Self-Intersections of Planar Curves, and Non-Commutative Divergence

Date: 

Tuesday, April 6, 2021, 10:00am

Location: 

Zoom

Alekseev

Location: Zoom https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Time: Tuesday, April 6, 2021, 10:00 AM (Eastern US), 15:00 (UK/Eire), 16:00 (Central Europe), 22:00 (China)

Title: Conjugation of Words, Self-Intersections of Planar Curves, and Non-Commutative Divergence

Abstract: The space spanned by homotopy classes of free oriented loops on a 2-manifold carries an interesting algebraic structure (a Lie bialgebra structure) due to Goldman and Turaev. This structure is defined in terms of intersections and self-intersections of planar curves. In the talk, we will explain a surprising link between the Gaoldman-Turaev theory and the Kashiwara-Vergne problem on properties of the Baker-Campbell-Hausdorff series. Important tools in establishing this link are the non-commutative divergence cocycle and a novel characterisation of conjugacy classes in free Lie algebras in terms of cyclic words. The talk is based on joint works with N. Kawazumi, Y. Kuno and F. Naef. 

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Attachments

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