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Paired classical and quantum knot invariants and a K-theory clue for Heisenberg quantization.
Student-Run Research Seminar| Speaker: | Jennifer Brown, UC Davis |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 24 2018, 12:10PM |
The beautiful AJ conjecture implies that the quantization of one knot invariant - the A-polynomial - kills another famous invariant, the colored Jone's polynomial.
We will introduce these two knot invariants before describing their conjectured pairing and the surprising appearance of algebraic k-theory.
The definition of the A-polynomial involves an affine variety - it's been speculated that a distinguished element coming from the K-theory of that variety's function field has 2-torsion whenever the A-polynomial has a unique quantization satisfying the AJ conjecture. This K-theoretic condition is largely mysterious but well supported by examples.
Register for pizza here.