Associate Professor,

Department of Mathematics,

Central Michigan University,

Mt. Pleasant, MI 48859,

USA.

E-mail: chakr2d@cmich.edu

I am a co-organizer of the TAG Seminar. Please do contact me if you would like to give a talk.

I am not teaching this semester (Fall 2019) since I am on sabbatical. Here is a list of courses I have taught at Central Michigan.

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.)

- A modified Morrey-Kohn-Hörmander identity and applications to the $\overline{\partial}$-problem. (Joint with Phil Harrington)
*Submitted*. - On an observation of Sibony To appear in
*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.*

- Hölder estimates for Cauchy-Type Integrals and proper holomorphic mappings of symmetric products (Joint with Evan Castle, David Gunderman, and Ellen Lehet) The research reported in this preprint was conducted during the NSF funded Research Experience for Undergraduates at Central Michigan University.
- Proper holomorphic self-maps of symmetric powers of balls (Joint with Master's student Christopher Grow; Grow received the best thesis award from CMU for his work and is currently pursuing a Ph D at Michigan State University)
*Archiv der Mathematik* - Curves of constant curvature and torsion in the the 3-sphere (Joint with then high-school student Rahul Sahay and then undergraduate student Jared Willams)
*Involve: a journal of mathematics.* Rahul is now an undergraduate at UC Berkeley, and Jared is pursuing a Ph D in physics at the University of Missouri.
- Fourier Representations in Bergman Spaces,
*Journal of Mathematical Analysis and Applications.*. (Joint with former Master's student Pranav Upadrashta based on his thesis. Currently, Pranav is pursuing a Ph D at SUNY Stony Brook.) - Automorphism groups of nilpotent Lie algebras associated with certain graphs (Joint with Meera Mainkar and undergraduate student Savannah Swiatlowski) To appear in
*Communications in Algebra* - Master's student Tanuj Gupta wrote a thesis on Extrinsic curvature of hypersurfaces in Hermitian space. Currently, Tanuj is a Ph. D. at Texas A&M university.
- Bergman kernels of elementary Reinhardt domains (Joint with Meera Mainkar and undergraduate students Austin Konkel and Evan Miller)
*Submitted*

- Special session at AMS meeting at Michigan State, March 2015
- Special session at Joint Math Meetings in Seattle, January 2016
- Midwest Several Complex Variables Conference, University of Toledo, OH, May 2016
- Special Session at the Mathematical Congress of the Americas, Montréal, Canada, July 2017
- Summer school at MSRI, Berkeley June 2018
- Workshop in Bangalore, India July 2019
- Midwest Several Complex Variables Conference, University of Michigan, Dearborn, MI October 2019

- Christine Laurent-Thiébaut
- Sönmez Şahutoğlu
- Rasul Shafikov
- Mei-Chi Shaw
- Gopala Krishna Srinivasan
- Kaushal Verma
- Yunus Zeytuncu