**Debraj Chakrabarti**

Indian Institute of Technology, Mumbai

September 9, 2010

**The Cauchy-Riemann Equations on a Product Domain**:
Solving the Cauchy-Riemann, or ($\overline{\partial}$) equations with estimates is a central question in multidimensional complex analysis.
For strongly pseudoconvex domains, or more generally for domains of finite type, such estimates are classical and go back to the work of Kohn. This approach fails for many interesting domains, for example, product domains. We discuss some new results (joint with Mei-Chi Shaw) regarding regularity of the solutions of the $\overline{\partial}$-equation on product domains.