Zsuzsanna Dancso (Sidney)
"Emergent" tangles and Kashiwara-Vergne solutions abstract
Abstract:
We\'ll introduce a three-dimensional realisation of the Goldman-Turaev Lie bialgebra as "emergent" tangles in handlebodies, with a commutator and a "vertical flip" operation. The name "emergent" refers to a quotient by the second step of a version of the Vassiliev iltration. The Kontsevich integral fortangles induces a homomorphic expansion for emergent tangles inhandlebodies, and thus for the Goldman-Turaev Lie bialgebra. This, in turn, translates to a Kashiwara-Vergne solution via work of Alekseev, Kawazumi, Kuno and Naef. It would be even better to deduce the Kashiwara-Vergne equations directly from the relations that a homomorphic expansion foremergent tangles must respect. If time allows, we\'ll discuss an ongoing attempt in this direction. This in some sense re-casts work of Alekseev-Naef and Massuyeau, and is joint with (subsets of) Dror Bar-Natan, Tamara Hogan, Yusuke Kuno, Jessica Liu, and Nancy Scherich.
15:30 • Université de Genève, Section de mathématiques, 7-9 rue du Conseil-Général, Room 1-07
Kevin Buzzard (Imperial College, London)
Abstract:
I will give a live demo of how to use the Lean interactive theorem prover, and discuss uses, and potential future uses, of such tools in teaching, research, and communication of mathematics.
17:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 7