Don Zagier: Holomorphic Quantum Modular Forms

Explore the concept of holomorphic quantum modular forms in this comprehensive lecture by Don Zagier, presented at the Hausdorff Center for Mathematics. Delve into the connection between these mathematical structures and number-theoretical problems, as well as quantum invariants of knots. Examine the weak modularity property of quantum modular forms and their holomorphic counterparts. Discover various applications and examples, including odd weight Eisenstein series for SL(2,Z) and a simplified interpretation of cohomology classes associated with Maass cusp forms. Gain insights from Zagier's collaborative work with Roelof Bruggeman and John Lewis as you unravel the intricacies of this fascinating mathematical topic.