A Non-Formal Formula for the Rankin Cohen Deformation Quantization

Explore a 26-minute conference talk from GSI that delves into the non-formal formula for the Rankin Cohen deformation quantization. Discover how Don Zagier's superposition of Rankin-Cohen brackets on the Lie group SL2(R) defines an associative formal deformation of the algebra of modular forms on the hyperbolic plane. Learn about the connections established between modular forms theory and regular foliations of co-dimension one. Examine Alain Connes and Henri Moscovici's proof that Rankin-Cohen's deformation gives rise to a formal universal deformation formula (UDF) for actions of the group ax + b. Investigate the realization of this UDF as a truncated Moyal star-product. Understand the method used to produce an equivariant intertwiner between the truncated Moyal star-product and a non-formal star-product on ax + b. Explore how the specific form of the intertwiner yields an oscillatory integral formula for Zagier's Rankin-Cohen UDF, addressing a question raised by Alain Connes.

A non formal formula for the Rankin Cohen deformation quantization