Welded Tangles and the Kashiwara-Vergne Groups

Zsuzsanna Dancso (The University of Sydney)

In this talk I will explain a general method of “translating” between a certain type of problem in topology, and solving equations in graded spaces in (quantum) algebra. I’ll talk through several applications of this method from the 90’s to today: Drinfel’d associators and parenthesised braids, Grothendieck-Teichmuller groups, welded tangles and the Alekseev-Enriquez-Torossian formulation of the Kashiwara-Vergne equations, and most recently, a topological description of the Kashiwara-Vergne groups. The “recent” portion of the talk is based on joint work with Iva Halacheva and Marcy Robertson (arXiv: 2106.02373), and joint work with Dror Bar-Natan (arXiv: 1405.1955).

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