Sary Drappeau: q-Pochhammer symbols and modularity

Abstract:

In a seminal paper, Zagier studied several examples of what he called “quantum modular forms”. They are maps \(f : \mathbb{Q} \to \mathbb{C}\) which satisfy sort-of modularity relations. One mysterious example came from quantum knot invariants, involving the q-Pochhammer symbol \((q)_n = (1-q)(1-q^2) \dotsb (1-q^n)\). We’ll talk about conjectures and recent works on this object.