The Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem
Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017
Location: SLMath: Eisenbud Auditorium
Galois theory
Galois orbits
Periods
torsors
Lie algebras
shuffle product
grt and GRT
derivators
associators
Lie bialgebras
14D24 - Geometric Langlands program (algebro-geometric aspects) [See also 22E57]
17B45 - Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
53C12 - Foliations (differential geometric aspects) [See also 57R30, 57R32]
Alekseev
It is conjectured that several graded Lie algebras coming up in different fields of mathematics coincide: the Grothendieck-Teichmueller Lie algebra grt related to the braid group in 3d topology, the double shuffle Lie algebra ds in the theory of multiple zeta values and the Kashiwara-Vergne Lie algebra kv in Lie theory. We are adding one more piece to this puzzle: it turns out that the Kashiwara-Vergne Lie algebra plays an important role in the Goldman-Turaev theory defined in terms of intersections and self-intersections of curves on 2-manifolds. This allows to define the Kashiwara-Vergne problem for surfaces of arbitrary genus. In particular, we focus on the genus one case and discuss the relation between elliptic kv and elliptic grt. The talk is based on a joint work with N. Kawazumi, Y. Kuno and F. Naef
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Alekseev
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