Department of Mathematics,

Central Michigan University,

Mt. Pleasant, MI 48859,

USA.

E-mail: chakr2d@cmich.edu

Vitae

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.)

- 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.* - 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)
*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). To appear in
*Pacific Journal of Mathematics*Austin received the Goldwater scholarship! - Master's student Pradeep Bihani wrote a thesis on String Kernel Based Text Source Classification, a foray into machine learning. The highlight of the project was the use of support vector machines to distinguish the tweets of Joe Biden and Donald Trump. Currently, Pradeep is employed by Intuit, Inc. , the makers of TurboTax and QuickBooks.
- Ph D student Anirban Dawn wrote a thesis on Laurent Series as Fourier Series. He currently teaches at the University of Tampa.
- Master's student Chase Bender wrote a thesis on the polarization identity of linear algebra. This paper (in
*Linear Algebra and Applications*) is partly based on his thesis. He is now a graduate student at Notre Dame. - Ph D student Rasha Almughrabi wrote a thesis on the computation of certain Bergman kernels. Here is her paper (to appear in
*Complex Analysis and Operator Theory*) explaining the intricate computation. - In summer 2023, undergraduate students Ishani Gaidhane, Jonathan Gregory and Mary Wright were jointly mentored by graduate student Isaac Cinzori and me on a project to extend Rasha's result to n dimensions. The results can be found in this paper.

- 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