# Debraj Chakrabarti

Department of Mathematics,
Central Michigan University,
Mt. Pleasant, MI 48859,
USA.
E-mail: chakr2d@cmich.edu

Vitae

## Teaching

Students may log into Blackboard for information related to their courses, including office hours.
Here is a list of courses I have taught at Central Michigan.

## Mathematics

My research interests are in Complex Analysis, more particularly in Several Complex Variables, which is basically the study of holomorphic functions (and other analytic objects) defined on complex manifolds of higher dimensions. This area of mathematics is closely related to differential and algebraic geometry on one hand and PDE (boundary value problems) on the other. An elementary introduction, giving the flavor of the area may be found in this popular article. (disclaimer: although most of the article in this link was written by me, the comments in the margins and a number of typos in the text were contributed by the publishers of the magazine where it appeared.)

### Publications and preprints

• Power series as Fourier Series (Joint with Anirban Dawn) To appear in Rocky Mountain Journal of Mathematics .
• Exact sequences and estimates for the $\overline{partial}$-problem. (Joint with Phil Harrington) Mathematische Zeitschrift .
• $L^p$-regularity of the Bergman projection on quotient domains (Joint with Chase Bender, Luke Edholm and Meera Mainkar). Canadian Journal of Mathematics .
• A modified Morrey-Kohn-Hörmander identity and applications to the $\overline{\partial}$-problem. (Joint with Phil Harrington) Journal of Geometric Analysis .
• On an observation of Sibony Proceedings of the AMS .
• Duality and approximation of Bergman spaces (Joint with Luke Edholm and Jeff McNeal) Advances in Mathematics .
• The restriction operator on Bergman spaces (Joint with Sönmez Şahutoğlu) Journal of Geometric Analysis. .
• On the $L^2$-Dolbeault cohomology of annuli (Joint with Mei-Chi Shaw and Christine Laurent-Thiébaut) Indiana University Mathematical Journal .
• Distributional Boundary Values: Some New Perspectives (Joint with Rasul Shafikov) Contemporary Mathematics. (Proceedings of the Conference on Analysis and Geometry in Several Complex Variables, Doha, Qatar, January 2015)
• Distributional boundary values of holomorphic functions on product domains. (Joint with Rasul Shafikov) Mathematische Zeitschrift.
• Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology Archiv der Mathematik .
• $L^p$ mapping properties of the Bergman projection on the Hartogs triangle (Joint with Yunus E. Zeytuncu) Proceedings of the AMS .
• Function theory and holomorphic maps on symmetric products of planar domains (Joint with Sushil Gorai.) Journal of Geometric Analysis.
• The $L^2$ cohomology of a bounded smooth Stein domain is not necessarily Hausdorff (Joint with Mei-Chi Shaw) Mathematische Annalen .
• Condition R and holomorphic mappings of domains with generic corners (Joint with Kaushal Verma) Illinois Journal of Mathematics.
• Condition R and proper holomorphic maps between equidimensional product domains (Joint with Kaushal Verma.) Advances in Mathematics.
• On a remarkable formula of Ramanujan (Joint with Gopala Krishna Srinivasan.) Archiv der Mathematik.
• Sobolev Regularity of the $\overline{\partial}$-equation on the Hartogs Triangle (Joint with Mei-Chi Shaw.) Mathematische Annalen
• A Class of Domains with noncompact $\bar{\partial}$-Neumann operator Proceedings of the AMS.
• $L^2$ Serre Duality on Domains in Complex Manifolds and Applications (Joint with Mei-Chi Shaw.) Transactions of the AMS.
• The Cauchy-Riemann Equations on Product Domains (Joint with Mei-Chi Shaw.) Mathematische Annalen.
• Spectrum of the complex Laplacian on product domains Proceedings of the AMS.
• CR Functions on Subanalytic Hypersurfaces (Joint with R. Shafikov.) Indiana University Mathematics Journal .
• Holomorphic Extension of CR Functions from Quadratic Cones (Joint with R. Shafikov) Mathematische Annalen
• Sets of Approximation and Interpolation in C for manifold-valued map Journal of Geometric Analysis.
• Coordinate neighborhoods of arcs and the approximation of maps into (almost) complex manifolds Michigan Math. J.