Quasimodular forms for the orthogonal group and Gromov-Witten theory
Georg Oberdieck (Heidelberg)

In this talk we begin by introducing quasimodular forms for orthogonal groups as constant terms of almost-holomorphic modular forms. For this we introduce orthogonal lowering and raising operators. Basic results are the description of the spaces of quasimodular forms in terms of vectorvalued modular forms and the interaction with the theta lift. In particular, we give a criterion when the theta lift of a quasimodular form is again quasimodular (it is not always the case). In the second part of the talk I will explain how these quasimodular forms appear in the Gromov-Witten theory of Enriques surfaces. They also want to appear in the Gromov-Witten theory of K3 surfaces, but actually more general automorphic objects there. Based on joint work with Brandon Williams.

Zoom (680 4828 0736, The password is the first Fourier coefficient of the modular j-function (as digits)).