Formal deformations: from modular to Jacobi through quasimodular forms

We give an overview of the notion of formal deformation of a commutative algebra and use it to propose an answer to the question What are Rankin-Cohen brackets? We construct formal deformations of the algebra of quasimodular forms after having built all their Poisson brackets. Then, we give different ways to construct formal deformations of the algebra of weak Jacobi forms and link these constructions with the one provided for quasimodular forms. These are joint works with YoungJu Choie, François Dumas, and François Martin.

Colloquium

Institute of Mathematical Research and Department of Mathematics, The University of Hong Kong, Hong Kong.