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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.)
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)
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
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.)
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. After graduation from Central Michigan, Pradeep first worked for Intuit, Inc. , the makers of TurboTax and QuickBooks, and now for Doordash.
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.