Working at the intersection of homogenization theory, spectral analysis in perforated domains, and numerical methods via boundary integral equations.
क्षितिज
सिन्हा
Department of Mathematics, Indian Institute of Technology Bombay
I am a PhD student in Mathematics at the Department of Mathematics, Indian Institute of Technology Bombay. My doctoral work is situated at a rich boundary between pure analysis and applied mathematics.
My research primarily focuses on Homogenization Theory within Partial Differential Equations. At present, I am investigating spectral problems arising in periodically perforated domains — structures that appear naturally in composite materials, porous media, and biological tissues.
In parallel, I am engaged in the numerical analysis of these problems using Boundary Integral Equations, bridging the analytical and computational dimensions of the field.
Quantitative periodic homogenization of parabolic equations with large drift and potential
Accepted · DCDS-B arXiv:2509.22003 ↗Homogenization of Three Species Reaction Diffusion Equation in Perforated Domains
Preprint arXiv:2603.26927 ↗Talks Given
Quantitative aspects of Homogenization of Elliptic PDEs in Periodic Settings
Doctoral Course (5.5 hrs) — Quantitative Theory of Homogenization Workshop, IIT Bombay
Feb 2025
Quantitative periodic homogenization of parabolic equations with large drift and potential
Stochastic Processes and Related Topics 2025 — IIT Gandhinagar
Sep 2025
Conferences & Schools Attended
NCMW — A Contemporary Course on Elliptic PDEs
TIFR–CAM, Bengaluru · Organized by Ali Hyder & Debabrata Karmakar
May–Jun 2024
Quantitative Theory of Homogenization
IIT Bombay · Organized by Harsha Hutridurga & S. Sivaji Ganesh
Feb 2025
Stochastic Processes and Related Topics 2025
IIT Gandhinagar · Organized by Chetan D. Pahlajani
Sep 2025
Partial Differential Equations
Aug–Dec 2024 & Aug–Dec 2025
Optimization
Jan–Apr 2025 & Jan–Apr 2026
I am open to discussions on homogenization theory, PDE analysis, numerical methods, and collaborative research. Feel free to reach out via email.
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