Generalized Fishburn numbers, torus knots and quantum modularity

Abstract: The Fishburn numbers are a sequence of positive integers with numerous combinatorial interpretations and interesting asymptotic properties. In 2016, Andrews and Sellers initiated the study of arithmetic properties of these numbers. In this talk, we discuss a generalization of this sequence using knot theory and the quantum modularity of the associated Kontsevich-Zagier series.

The first part is joint work with Colin Bijaoui (McMaster), Hans Boden (McMaster), Beckham Myers (Harvard), Will Rushworth (McMaster), Aaron Tronsgard (Toronto) and Shaoyang Zhou (Vanderbilt) while the second part is joint work with Ankush Goswami (RISC).

number theory

Audience: researchers in the topic

( slides )

Warsaw Number Theory Seminar