Abstract:
Torus knots are long known to satisfy a special relation between their HOMFLY-PT and Kauffman polynomials, which has a peculiar implication in the context of Topological Strings. In this talk, I will describe infinite families of hyperbolic knots and links that enjoy the same property. These were found via a physics-inspired tool called the Harer-Zagier (HZ) transform, which is a version of the Laplace transform that maps the HOMFLY-PT polynomial into a rational function. It is conjectured that whenever the latter is factorisable, the HOMFLY-PT-Kauffman relation occurs. I will explain how some steps towards a proof of this conjecture can be made, at least for 3-strand braids, by expanding these two-variable link polynomials in terms of characters.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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