2008-11-14

Xiang Tang, University of Washington (St. Louis)

Rankin-Cohen Brackets and Formal Quantization

Recently Hopf algebras have played a role in several areas of mathematics and physics. The fact that the same Hopf algebra was useful in the study of foliations, renormalization in quantum field theory, and number theory has led to interesting discoveries. Inspired by the Rankin-Cohen brackets on modular forms, Connes and Moscovici constructed a universal deformation formula for the Hopf algebra associated to a codimension one foliation. In this talk, we will explain how to use differential geometry to understand their deformation and various structures involved. In particular, we will show that the Rankin-Cohen deformation is closely related to the Weyl-Moyal product.