Research

My research interests are in the Numerical Analysis and solution of Partial Differential Equations (PDE's) and high performance computing. My current focus is on the design and analysis of accurate multiscale multiphysics numerical methods for massively parallel simulations of coupled fluid flow and poroelastic interations. Previously I have also worked on topics in analytical PDE's. Mainly these include infinity harmonic functions and convex integration. 

Selected Reports :  

1. Analyzing the Influence of Virtual Care Management on Patient Health Outcomes and Risk Stratifying Chronic Kidney Disease Patients for Stage Degeneration. Mathematics in Industry Reports (MIIR), SIAM Mathematical Problems in Industry Workshop.

2. A numerical and stochastic approach for modeling cell population dynamics in colonic crypts undergoing asymmetric cell divisions. Graduate Student Mathematical Modelling Camp (GSMMC) by SIAM.

3. Weak Topology and Completion in Sobolev Spaces

4. Fractional Maps in Cryptography

• Lipschitz Extension Problem (Masters Thesis Defence), IISER Pune, June 2021.

• Infinity Harmonic Functions and Calculus of Variations, Analysis and Geometry Seminar, Math Department IIT Gandhinagar, Jan 2022.

You can find a brief description of my past projects in my CV.