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What else can you do with solvable approximations?

McGill University HEP Seminar, February 2, 2017

Abstract. Recently, Roland van der Veen and myself found that there are sequences of solvable Lie algebras "converging" to any given semi-simple Lie algebra (such as $sl_2$ or $sl_3$ or $E8$). Certain computations are much easier in solvable Lie algebras; in particular, using solvable approximations we can compute in polynomial time certain projections (originally discussed by Rozansky) of the knot invariants arising from the Chern-Simons-Witten topological quantum field theory. This provides us with the first strong knot invariants that are computable for truly large knots.

But $sl_2$ and $sl_3$ and similar algebras occur in physics (and in mathematics) in many other places, beyond the Chern-Simons-Witten theory. Do solvable approximations have further applications?

Handout: SolvApp.html, SolvApp.pdf, SolvApp.png.

Talk Video.

Links: gwu ind ld akt.

Sources: pensieve.