Using heat equation methods, the index of an elliptic operator can be computed by a local formula. In this series of lectures, we will review the necessary analysis for defining the index of an elliptic operator, and derive a local formula for the index.

In this three lecture series I will give a general introduction to CR functions. I will start with basic definitions and examples. Then I will give an overview of classical results on holomorphic extension and approximation of CR functions. In the last lecture I will discuss the recent joint work with Chakrabarti on CR functions on singular hypersurfaces.

Using heat equation methods, the index of an elliptic operator can be computed by a local formula. In this series of lectures, we will review the necessary analysis for defining the index of an elliptic operator, and derive a local formula for the index.

In this talk, we will review the deformation and Hochschild cohomology of associative algebras and generalize it to A-infinity algebras. One simple application will be given afterwards. This is based on my extended master thesis in China, which can be downloaded at http://www.math.uwo.ca/~ewu22/notes.html. Slides will be used in this talk.