In Zagier's paper titled "quantum modular forms", one of the first examples of quantum modular form is related to the q-series $$ \sigma(q)=1+\sum_{n=0}^\infty (-1)^n q^{n+1} (q)_n $$ from Ramanujan's "Lost" Notebook. In this talk, I will discuss the resurgent structure of the formal power series associated with the q-series $\sigma(q)$: it is a simple resurgent structure which conjecturally encodes the modularity properties already studied by Zagier. Furthermore, the same resurgent structure appears when considering formal power series associated to other q-series, such as the Kontsevich--Zagier q-series for trefoil and the q-series coming from the fermionic spectral traces of quantum-mechanical operators related with the quantization of the mirror curve of toric CY 3-folds (recently studied by C. Rella arXiv:2212.10606). Hence we expect to find analougus modularity properties by studying their resurgent structures.
De Maxim Kontsevich
De Maxim Kontsevich
De Philip Boalch
De Kohei Iwaki
De Maxim Kontsevich
De Maxim Kontsevich
De Jorgen Ellegaard Andersen
De Sergei Gukov
De Jorgen Ellegaard Andersen
De Jorgen Ellegaard Andersen
De Veronica Fantini
