Speaker
Description
Multiple Eisenstein series, introduced in 2006 by Gangl-Kaneko-Zagier, form a bridge between multiple zeta values and classical Eisenstein series. In this talk, I will discuss recent developments and conjectures concerning these series, with a focus on a possible sl2-algebra structure. By this, we mean an algebra A equipped with an injective Lie algebra homomorphism from the three-dimensional Lie algebra sl2 into the derivation algebra Der(A). A classical example is the algebra of quasimodular forms, which carries three natural derivations satisfying the sl2 commutation relations. The algebra of multiple Eisenstein series contains the quasimodular forms as a subalgebra. I will present a conjectural framework suggesting that the sl2-structure on quasimodular forms extends naturally to this larger algebra. Finally, I will outline a dimension conjecture for the space of multiple Eisenstein series, which indicates that the presence of an sl2-structure might be the key feature distinguishing them from multiple zeta values.
