Parveen Kumar | Mathematics

About Me

I am a PhD Research Scholar in the Department of Mathematics at Indian Institute of Technology Ropar. I am working under the supervision of Dr. Manmohan Vashisth . My research focuses on inverse problems for partial differential equations, particularly uniqueness, reconstruction and stability results for coefficient identification problems.

Research Interests

Inverse Problems

Recovery of unknown coefficients and parameters from boundary measurements.

Partial Differential Equations

Analysis of heat equations, wave equations, Schrödinger equations and related PDE systems.

Integral Geometry

Inversion of the ray transform for establishing uniqueness and stability estimates in inverse problems.

Publications & Preprints

Reconstruction of Time-Dependent Coefficients in a Semilinear Dynamical Schrödinger Equation

Parveen Kumar, Gen Nakamura, and Manmohan Vashisth

Submitted, arXiv:2606.17023 (2026)

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Stable determination of time-dependent coefficients in a reaction-diffusion-convection system

Rahul Bhardwaj and Parveen Kumar

Submitted, arXiv.2608.07190 (2026)

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A partial data coefficient identification inverse problem for a semilinear damped wave operator

Mandeep Kumar, Parveen Kumar, and Manmohan Vashisth

Submitted, arXiv:2608.29918 (2026)

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Stability in the determination of the coefficients for coupled relativistic Schrödinger system

Nitesh Kumar, Parveen Kumar, and Tanmay Sarkar

Submitted, arXiv.2610.15013 (2026)

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Experience

Indian Institute of Technology Ropar

Advanced Instructional School (AIS) on Analysis and Partial Differential Equations

Teaching assistant
May 26–June 14, 2025

Indian Institute of Technology Jammu

Junior Research Fellow (JRF)
March 2022- January 2023

Principal Investigator: Dr. Manmohan Vashisth
Title of Project: Inverse coefficients and shape identification problems for PDEs

Education

Indian Institute of Technology Ropar

Doctor of Philosophy (Ph.D.) in Mathematics
2024 - Present

Supervisor: Dr. Manmohan Vashisth

Visvesvaraya National Institute of Technology Nagpur

Master of Science(M.Sc.) in Mathematics
2018 - 2020

Pt. Neki Ram Sharma Govt. College (affiliated by Maharshi Dayanand University, Rohtak)

Bachelor of Science Honours(B.Sc.) in Mathematics
2014 - 2017

Talks & Events

Annual Inverse Meet (AIM 2026)

Indian Institute of Technology Bombay
September 18 - September 20, 2026

Talk title: Reconstruction of time-dependent coefficients in a semilinear dynamical Schrödinger equation

Summer School on Inverse Problems

TIFR Centre for Applicable Mathematics, Bengaluru
July 6 - July 17, 2026

12th Applied Inverse Problems Conference (AIP 2025)

Getulio Vargas Foundation – FGV EMAp, Rio de Janeiro, Brazil
July 28 - August 1, 2025

Talk title: Determining the time-dependent convection term and matrix-valued potential in a heat equation from partial data.

Workshop on Multi-scale Analysis cum Conference on Differential Equations

Indian Institute of Technology Ropar
February 26 - March 2, 2024

Advanced Instruction School on Elliptic and Parabolic PDEs

Indian Institute of Science, Bengaluru
December 4 - December 23, 2023

Workshop on Advances in Differential Equations: Theory and Computation

Thapar Institute of Engineering and Technology, Patiala
October 2 - October 7, 2023

NCM - Instructional School for Teachers on Ordinary Differential Equations and Dynamical Systems

Indian Institute of Technology Mandi
June 26 - July 8, 2023

Contact

Seat Number: RS-A3-010A
Civil Side, 3rd floor, Block-A (SAB)

Indian Institute of Technology Ropar
Nangal Road, Rupnagar (Ropar), Punjab, India - 140001

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