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Knots, (extremal) A-polynomials, and BPS invariants

Presented by: 
Piotr Kucharski
Tuesday 11th April 2017 - 13:30 to 14:30
INI Seminar Room 1
Co-author: Piotr Sulkowski (University of Warsaw, Caltech)

In this talk I will introduce a new class of algebraic curves called extremal A-polynomials of a knot and use it to describe BPS invariants introduced by Labastida, Marino, Ooguri, and Vafa.

I will present results obtained from the analysis of both classical and quantum extremal A-polynomials. The first lead to exact formulas for BPS invariants imposing nontrivial integrality statements in number theory. The latter enabled us to construct the combinatorial model for calculating BPS invariants.

I will also indicate how these results relate to the formalism of quivers introduced in the talk by Piotr Sulkowski.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons