### Speaker

Prof.
Sergei Gukov
(Caltech)

### Description

Quantization of planar algebraic curves naturally enters many branches of physics and mathematics. For example, quantization of the zero locus of the A-polynomial of a knot gives the best known way to package an infinite set of colored Jones invariants of that knot into a single equation. Quantization of such A-polynomial curves is similar and, in some examples even identical, to quantization of spectral curves of trigonometric integrable systems. The latter lead to Baxter equations. Surprisingly, however, if the same planar curve appears as the A-polynomial of a knot and the spectral curve of a trigonometric integrable system, the result of its ``quantization'' in these two frameworks will be different.

### Primary author

Prof.
Sergei Gukov
(Caltech)