I am a fifth-year PhD candidate in the Department of Mathematical Sciences at Montana State University, advised by Blair Davey. I expect to finish in May 2027.
My research is in analysis and partial differential equations, with a focus on quantitative unique continuation for elliptic PDEs. My dissertation proves vanishing order estimates for generalized Schrödinger equations with W^{1,p} potentials. I am also interested in harmonic analysis, fractal geometry and geometric measure theory, ergodic theory, and probability.
Before MSU, I earned an MS in Mathematics through the International Mathematics Master (IMM) program at COMSATS University Islamabad, where I wrote a thesis on self-similar and self-affine sets under Thomas Jordan (University of Bristol). I also hold a BS in Economics and Mathematics from IBA Karachi.
Recognition
Teaching Excellence Award, MSU Mathematical Sciences, 2026
Outstanding Graduate Teaching Award, MSU Mathematical Sciences, 2024
Outstanding Graduate Student Award, MSU Mathematical Sciences, 2023
International Mathematics Master Fellowship, 2020-2022
When I'm not doing math, I'm usually hiking in the mountains or playing board games and outdoor games with friends.