Knots give rise (via complex Chern-Simons theory) to matrices of q-series, (formal power series with integer coefficients) with remarkable combinatorial, arithmetic and analytic properties, which define, in particular, holomorphic functions in the complex plane minus a ray. These are examples of 'holomorphic quantum modular forms'. We will explain the main ideas with examples of the two simplest hyperbolic knots. Joint work with Rinat Kashaev, Don Zagier, Jie Gu and Marcos Marino (in various collaborations).
Lien bbb : https://bbb.lipn.univ-paris13.fr/b/ban-kpe-96w