Description:

Title: Polylogarithms and Habiro cohomology

Abstract: In their recent work, Garoufalidis, Scholze, Wheeler, and Zagier have defined the notion of Habiro ring of a number field, in order to capture the arithmetic behaviour of certain q-series coming from 3-manifold topology. These Habiro rings are global invariants of number fields, and are reminiscent of a more general theory, still under development, of Habiro cohomology. In this talk, I want to explain how certain constructions from number theory can also be lifted to this new setting. More precisely, I will explain how a refinement of Bhatt and Lurie's prismatic logarithm can be used to produce natural q-polylogarithm classes in this context. This is based on joint work with Quentin Gazda.