Quantum q-series identities

Abstract: As analytic identities, classical $q$-series identities like the Rogers-Ramanujan identities are equalities between functions for $|q|<1$. In this talk we discuss another type of $q$-series identity, called a quantum q-series identity, which is valid only at roots of unity. We note some examples from work of Cohen, Bryson-Ono-Pitman-Rhoades, and Folsom-Ki-Vu-Yang, and then show how these and many more quantum identities follow from classical q-hypergeometric transformations. In the second part of the talk we discuss examples of quantum q-series identities arising from knot theory.

number theory

Audience: researchers in the topic

EIMI Number Theory Seminar

Series comments: Password: the number of quadratic nonresidues modulo 23