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Dror Bar-Natan:
Talks:
# Trees and Wheels and Balloons and Hoops and Why I Care

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## Colloquium, University of Toronto, March 6, 2013

**Abstract.** I will be talking about an invariant ζ. For the
first 15 minutes I will be talking about its target space, algebra (trees and
wheels, or free Lie algebras and cyclic words). For the next 15 minutes I will
talk about its domain space, topology (knotted balloons and hoops in 4-space).
And in the remaining time I will tell you why I care, though with little
detail: It is the universal solution to a topological problem and it has many
siblings (who talk to each other). It is explicitly computable. Its target
space is in itself a space of "universal formulas in Lie algebras" (that's
"the miracle"). It seems to be a complete(?) evaluation a certain gauge
theory. It is related to a deep conjecture in Lie theory proven by Alekseev
and Meinrenken. It has even-better-computable specializations, including one
which is an "ultimate Alexander invariant". And plenty of work remains to be
done.

**Talk video.** .

There's also a **paper in progress**.