I am a graduate student at Michigan State University (MSU), and I expect my PhD in Mathematics in May 2020. My thesis advisor is Dr. Russell Schwab. My curriculum vitæ can be found here.
My research focuses on integro-differential operators associated with certain partial differential equations and their properties. In particular, I study:
- Degenerate elliptic equations on a half-space and their Dirichlet to Neumann (D-to-N) maps expressed as integro differential operators, along with the properties of the measure associated with this representation.
- Free boundary problems (existence and uniqueness of solutions) whose boundary can be captured as the graph of a function over the on the d-dimensional sphere, where the boundary is a hypersurface that may not be regular.
Details about my work can be found in my research statement
I have been teaching as a Graduate Assistant at MSU since Fall 2014, and before that I worked as a lecturer at Don Bosco Institute of Technology, Bombay, India (2012-2014).
- A list of former and current teaching assignments can be found on my teaching page and also on my CV . Details about my teaching philosophy can be found in my teaching philosophy statement.
- I am currently working on completing the Graduate Certification in College Teaching Program at MSU and I expect to complete it by May 2020.
- I have recently taken a keen interest in the field of Mathematics Education. I have been working with a research group under Dr. Shiv Karunakaran at MSU on a project regarding the Transitions to Proofs class. I am also taking the course, 'Psychology and Pedagogy in Math' (CEP913) at MSU this semester (Fall 2019) to broaden my knowledge of the field.