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On Quantizing the A-polynomial
Student-Run Research Seminar| Speaker: | Jenny Brown, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~brown/ |
| Location: | 2112 MSB |
| Start time: | Thu, Feb 17 2022, 12:10PM |
The beautiful AJ conjecture predicts that a (yet-undefined) quantization of one knot invariant - the A-polynomial - annihilates another famous invariant, the colored Jones polynomial. In other words, it's expected that the A-polynomial has a non-commutative version $\hat{A}$ which behaves like a differential operator that can act on the colored Jones polynomial $J$. The relationship $\hat{A} J = 0$ gives the conjecture its name.
This conjecture was formulated independently by both mathematicians and physicists, and is open but well supported.
The A-polynomial is constructed from the character variety of a knot's complement. We will describe recent work on quantizing this construction using skein theory. This approach is inspired by the physical formulation of the conjecture.