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 CMU Analysis and Geometry Seminar. Please do contact me if you would like to give a talk.

I also the supervisor of the Central Michigan Math Department Problem of the Week. If you have solved this week's problem, please send me the solution, or take it to the math department office! There are prizes for CMU undergraduates!

In summer 2019 I am co-organizing a workshop in Bangalore, India, on Several Complex Variables.

- Fall 2018:
- Math 130 (Precalc): MTuWTh 9:00 AM-- 9:50 AM, Pearce 226.

- Spring 2018:
- Math 533 (Advanced Calculus -II): MW 3:30 -- 4:45 pm, Pearce 108.
- Math 737 (Topics in Analysis): MW 5:00 -- 6:15 pm, Pearce 224.

- Fall 2017:
- Math 233 (Calculus 3): MWTuWTh 11am -- 11:50 am, Pearce 228 .

- Spring 2017:
- Math 637 (Second semester complex analysis): M W 2:00 PM-3:15 PM, Pearce 203.
- Math 632 (Real Analysis) M W 03:30 PM-03:45 PM, Pearce 203

- Fall 2016:
- Math 233 (Calculus-- 3): M Tu W Th 10:00 AM-10:50 AM, Pearce 226.
- Math 634 (Fourier Analysis) M W 02:00 PM-03:15 PM, Pearce 223

- Summer 2016:
- 2 weeks topics course ''Several Complex Variables'', 16th to 27th May: M Tu W Th F 02:00 PM-03:50 PM, Pearce 203

- Spring 2016:
- Math 232 (Linear Algebra and Differential Equations): Tu Th 9:30am to 10:45 pm, Dow 107 .

- Fall 2015:
- Math 632 (Real Analysis): M W 02:00 PM-03:15 PM. Pearce 223.
- Math 644 (Differential Geometry) Tu Th 09:30 AM-10:45 AM. Pearce 224.

- Summer 2015:
- Math 696 D-- 2 weeks topics course ''Laplace's equation'' 29th June to 10th July. MTWTF 1:00 to 2:50 pm. Pearce 108.

- Spring 2015:
- Math 636 (Graduate Complex Analysis) 2:00 pm to 3:15 pm, Pearce 108.
- Math 545 (Topology): MW 3:30 pm to 4:45 pm, Pearce 108.

- Fall 2014:
- Math 632 (Real Analysis): Tu Th 12:30pm to 1:45 pm, Pearce 108.

- Spring 2014:
- Math 233 (Calc 3): MTWTF 11:00 am to 11:50 am, Dow 136

- Fall 2013:
- Math 132 (Calculus 1): Mon/Wed 1:00 pm to 2:50 pm , Pearce 136
- Math 625 (Associative Rings): Tues/Thurs 12:30 pm to 1:45 pm, Pearce 224

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 To appear in
*Journal of Mathematical Analysis and Applications.*. (Joint with former Master's student Pranav Upadrashta based on his thesis. Pranav is pursuing a Ph D at SUNY Stony brook since Fall 2018) - Automorphism groups of nilpotent Lie algebras associated with certain graphs (Joint with Meera Mainkar and undergraduate student Savannah Swiatlowski)
*Submitted for publication* - Master's student Tanuj Gupta wrote a thesis on Extrinsic curvature of hypersurfaces in Hermitian space. Tanuj is starting a Ph. D. at Texas A&M university in Fall 2019.

- Special session at AMS meeting at Michigan State, March 2015
- Special session at Joint Math Meetings in Seattle, January 2016
- Midwest Several Complex Variable 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

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