PhD Researcher · Mathematics

Kshitij
Sinha

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

01

About

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.

  • Homogenization of PDEs
  • Spectral Problems in Perforated Domains
  • Boundary Integral Equations
  • Numerical Analysis
  • Parabolic Equations with Drift
02

Education

PhD in Mathematics
Indian Institute of Technology Bombay
2023 — Present
MSc in Mathematics
Indian Institute of Technology Kanpur
2020 — 2022
BSc in Mathematics
Banaras Hindu University, Varanasi
2017 — 2020
03

Publications

[1]

Quantitative periodic homogenization of parabolic equations with large drift and potential

Kshitij Sinha

Accepted · DCDS-B arXiv:2509.22003 ↗
[2]

Homogenization of Three Species Reaction Diffusion Equation in Perforated Domains

Saumyajit Das, Kshitij Sinha

Preprint arXiv:2603.26927 ↗
04

Talks & Conferences

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

05

Teaching Experience

MA515

Partial Differential Equations

Aug–Dec 2024 & Aug–Dec 2025

SI416

Optimization

Jan–Apr 2025 & Jan–Apr 2026

06

Contact

I am open to discussions on homogenization theory, PDE analysis, numerical methods, and collaborative research. Feel free to reach out via email.

Download CV ↓