Derivations on formal multiple Eisenstein series

• Applicant: Dr. Annika Burmester, since 11/2025
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 555602108

We study certain q-analogues of multiple zeta values related to partitions, (quantum) modular forms and enumerative geometry. In previous joint work with Bachmann, we found that the sl2-action by derivations on quasimodular forms extends to a formalized version of this space of q-analogues. Our main objective in this project is to describe the full Lie algebra of derivations acting on formal multiple Eisenstein series. We expect that this mimics the well-studied situation of derivations on motivic multiple zeta values, where such derivations are known to be closely related to the Hopf algebra structure. This project includes obtaining explicit formulas for the derivations in every weight. Moreover, we aim to prove these conjectural results.

• DFG Programme: Research Grants
• International Connection: Japan
• Cooperation Partner: Professor Dr. Henrik Bachmann
• Co-Investigator: Dr. Steven Charlton
• Ehemaliger Antragsteller: Dr. Jan-Willem van Ittersum, until 11/2025