Research

Research articles

1. Nitesh Kumar, Tanmay Sarkar and Manmohan Vashisth; Boundary determination of coefficients appearing in a perturbed weighted p-Laplace equation, Submitted (arXiv).
2. Rohit Kumar Mishra and Manmohan Vashisth; Inverse problem for a time-dependent Convection-diffusion equation in admissible geometries, Submitted (arXiv).
3. Maarten V. de Hoop, Takashi Furuya, Ching-Lung Lin, Gen Nakamura and Manmohan Vashisth; Local recovery of a piecewise constant anisotropic conductivity in EIT on domains with exposed corners, Inverse Problems, 39 (2023), no. 2, Paper No. 025005, 26 pp. (IP-2023). PDF
4. Gen Nakamura, Tanmay Sarkar and Manmohan Vashisth; Reconstruction for the time-dependent coefficients of a quasilinear dynamical Schroedinger equation, Preprint (arXiv).
5. Soumen Senapati and Manmohan Vashisth; Stability estimate for a partial data inverse problem for the convection-diffusion equation, Evolution Equations and Control Theory, Vol. 11, No. 5, October 2022, pp. 1681–1699. (EECT-2021) PDF
6. Manmohan Vashisth; Unique determination of the damping coefficient in the wave equation using point source and receiver data, Submitted (arXiv).
7. Gen Nakamura, Manmohan Vashisth and Michiyuki Watanabe; Inverse Initial Boundary Value Problem for a Non-linear Hyperbolic Partial Differential Equation, Inverse Problems, Volume 37 (2020) no. 1, 015012. (IP-2020) PDF
8. Guang-Hui Hu, Manmohan Vashisth and Jiaqing Yang; Inverse time-harmonic electromagnetic scattering from coated polyhedral scatterers with a single far-field pattern, SIAM Journal on Applied Mathematics, Volume 81, (2021) no. 1, 25–46.(SIAP-2020) PDF
9. Ibtissem Ben Aïcha, Guang-Hui Hu, Manmohan Vashisth and Jun Zou; Uniqueness for time-dependent inverse problems with single dynamical data, Journal of Mathematical Analysis and Applications, Volume 497, Issue 2, (2021), 124910. (JMAA-2020) PDF
10. Guang-Hui Hu and Manmohan Vashisth; Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave, Inverse Problems, Volume 36 (2020) no. 10, 105004. (IP-2020) PDF
11. Venkateswaran P. Krishnan, Soumen Senapati and Manmohan Vashisth; A uniqueness result for light ray transform on symmetric 2-tensor fields, Journal of Fourier Analysis and Applications Volume 26, 40 (2020). (JFAA-2020) PDF
12. Rohit Kumar Mishra and Manmohan Vashisth; Determining the time dependent matrix potential appearing in a wave equation from partial boundary data, Applicable Analysis Volume 100 (2021) No. 16, 3492-3508. (AA-2020) PDF
13. Cătălin I. Cârstea, Gen Nakamura and Manmohan Vashisth; Reconstruction for the coefficients of a quasilinear elliptic partial differential equation, Applied Mathematics Letters, Volume 98, December 2019, Pages 121-127. (AML-2019) PDF
14. Suman Kumar Sahoo and Manmohan Vashisth; A partial data inverse problem for the convection-diffusion equation, Inverse Problems and Imaging, Volume 14, No. 1, Pages 53–75.(IPI-2020) PDF
15. Manmohan Vashisth; An inverse problem for the wave equation with source and receiver at distinct points, Journal of Inverse and Ill-posed Problems, Volume 27, Issue 6, Pages 835–843.(JIIP-2019) PDF
16. Venkateswaran P. Krishnan and Manmohan Vashisth; An inverse problem for the relativistic Schroedinger equation with partial boundary data, Applicable Analysis, Volume 99 (2020), No. 11, 1889-1909. (AA-2019) PDF

Research grants

• Startup Research Grant (SRG) of amount Rs. 13,01,344/-, funded by Science and Engineering Research Board, Department of Science and Technology (SERB-DST) India from December, 2021 to December, 2023.

Collaborators

1. Ibtissem Ben Aïcha (Higher Institute of Preparatory Studies in Biology and Geology in Soukra, Tunisia)
2. Cătălin I. Cârstea (Sichuan University, Sichuan, China)
3. Takashi Furuya (Hokkaido University, Japan)
4. Guang-Hui Hu (Nankai University, Tianjin, China)
5. Maarten V. de Hoop (Rice University, USA)
6. Venkateswaran P Krishnan (TIFR Centre for Applicable Mathematics, Bengaluru, India)
7. Ching-Lung Lin (National Cheng Kung University, Taiwan)
8. Rohit Kumar Mishra (Indian Institute of Technology, Gandhinagar, India)
9. Gen Nakamura (Hokkaido University, Sapporo, Japan)
10. Suman Kumar Sahoo (University of Jyvaskyla, Finland)
11. Tanmay Sarkar (Indian Institute of Technology, Jammu, India)
12. Soumen Senapati (TIFR Centre for Applicable Mathematics, Bengaluru, India)
13. Jiaqing Yang (Xi'an Jiaotong University, Xi'an, China)
14. Michiyuki Watanabe (Okayama University of Science, Japan)
15. Jun Zou (The Chinese University of Hong Kong, Hong Kong)

Research visits

• Indian Institute Technology, Gandhinagar, India (IIT-GN) during November 28 - December 8, 2022, for a collaborative research with Dr. Rohit Kumar Mishra.
• Indian Institute Technology, Gandhinagar, India (IIT-GN) during April 4-21, 2022, for a collaborative research with Dr. Rohit Kumar Mishra.
• Indian Institute of Science Education and Research, Bhopal, India (IISER-B) during March 5-31, 2020, for a collaborative research with Dr. Manas Kar.
• Indian Institute of Science Education and Research, Bhopal, India (IISER-B) during February 17-24, 2020, for a collaborative research with Dr. Manas Kar.
• TIFR Centre Applicable Mathematics, Bengaluru, India (CAM) during February 9-16, 2020, for a collaborative research with Professor Venkateswaran P Krishnan.
• Hokkaido University, Sapporo, Japan (HOKUDAI) during January 11-31, 2020, for a collaborative research with Professor Gen Nakamura (Emeritus Professor at Hokkaido University).
• Hokkaido University, Sapporo, Japan (HOKUDAI) during April 30 - May 25, 2019, for a collaborative research with Professor Gen Nakamura (Emeritus Professor at Hokkaido University).
• Hokkaido University, Sapporo, Japan (HOKUDAI) during March 10-31, 2018, for a collaborative research with Professor Gen Nakamura (Emeritus Professor at Hokkaido University).
• Beijing Computational Science Research Center (CSRC), Beijing, China during February 4-9, 2018.
• Nanyang Technological University, Singapore (NTU) during January 22-27, 2018, for participating in Global Young Scientists Summit (GYSS-2018).
• Hokkaido University, Sapporo, Japan (HOKUDAI) during June 3 - July 2, 2017, for a collaborative research with Professor Gen Nakamura (Emeritus Professor at Hokkaido University).

Talks and conference presentations

1. Math Colloquium at IISER, Mohali, Punjab, India on November 15, 2023. (Talk title: Fundamental solutions to PDEs and inverse problems).
2. Mathematics Colloquium at IIT, Jammu, J&K, India on May 26, 2023. (Talk title: Lagrange multiplier method and its applications in linear algebra).
3. One Day Conclave on National Mathematics Day, 2022, organised by the Department of Mathematics, Cluster University of Jammu, J&K, India, on December 22, 2022. (Talk title : Gamma function and its applications).
4. Online seminar talk at Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN) Université de Tunis El Manar, Tunisia,on April 14, 2021. (Talk title : Inverse boudary value problems for nonlinear PDEs) (Video link).
5. Indian Institute of Science Education and Research (IISER-B) Bhopal, India, on March 6, 2020. (Talk title : A partial data inverse problem for the Convection-diffusion equation).
6. Indian Institute of Science Education and Research (IISER-B) Bhopal, India, on February 24, 2020. (Talk title : Inverse problems related to pde and integral geometry).
7. TIFR Centre Applicable Mathematics, (CAM) Bengaluru, India, on February 14, 2020. (Talk title : A partial data inverse problem for the Convection-diffusion equation).
8. RIMS Workshop on "Analysis of inverse problems through partial differential equations and related topics" (RIMS-2020) during January 8-10, 2020, at Research Institute for Mathematical Sciences, Kyoto University, Japan. (Talk title : Reconstruction for the coefficients of a quasilinear elliptic partial differential equation).
9. Conference on Modern Challenges in Imaging, In the Footsteps of Allan MacLeod Cormack, On the Fortieth Anniversary of his Nobel Prize (Imaging-2019) during August 5-9, 2019, at Tufts University, Medford, Massachusetts, USA. (Talk title : A uniqueness result for a light ray transform of two tensor field).
10. Annual International Conference "Days on Diffraction" (DD-2019) during June 3-7, 2019, at St. Petersburg Branch of the Steklov Mathematical Institute, Russia. (Talk title : Reconstruction for the coefficients of a quasilinear elliptic partial differential equation).
11. A mini-workshop on inverse problems and PDEs, organised by Prof. Guang-Hui Hu at Beijing Computational Science Research Center (CSRC), Beijing, China, On December 10, 2018. (Talk title: Some inverse problems in hyperbolic partial differential equations).
12. The 9th International Conference on Inverse Problems and Related Topics (ICIP-2018) during August 13-17,2018, Singapore, organised by National University of Singapore (NUS). (Talk title: Inverse boundary value problems for non-linear hyperbolic PDE).
13. Beijing Computational Science Research Center (CSRC), Beijing, China on February 7, 2018. (Talk title : A partial data inverse problem for the Covection-diffucion equation).
14. Conference on Recent Developments in Partial Differential Equations (CAM) during Aug 18-19, 2017, organised by TIFR Centre for Applicable Mathematics (TIFR-CAM), Bangalore, India on the Occasion of 10th year celebration of TIFR-CAM at Yelhanka Campus. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
15. Hokkaido University, Sapporo, Japan (HOKUDAI) on June 16, 2017. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
16. The 9th International Conference on Applied Inverse Problems (AIP-2017) during May 29 - June 2, 2017, Hangzhou, China, organised by School of Mathematical Sciences, Zhejiang University Hangzhou, China. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
17. International Conference of The Indian Mathematics Consortium (TIMC) in cooperation with American Mathematical Society (AMS) (BHU-2016) during December 13-17, 2016, BHU-Varanasi, India. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
18. International conference on Mathematical Analysis and its Applications (ICMAA-2016) during November 28 - December 2, 2016, IIT-Roorkee, India. (Talk Title : Inverse Problems for Wave Equation in 3-D with Under-determined Data).
19. The 8th International Conference on Inverse problems: modeling and simulation (IPMS-2016) during May 23-28, 2016, Turkey, organised by Izmir University, Turkey. (Talk Title : Inverse problems for wave equation with under-determined data).
20. Airbus project meeting talk in 2016, TIFR Centre for Applicable Mathematics, Bangalore, India. (Talk Title : Inverse problems for wave equation with source and receiver at distinct points).
21. In-house symposium Talk on August 5, 2015 in TIFR Centre for Applicable Mathematics, Bangalore, India. (Talk Title : Inverse Problems in Hybrid Imaging).

Teaching

Instructor (at IIT Ropar)

1. Linear Algebra, Integral Transforms and Special Functions (MA102) (jointly with Dr. Tapas Chatterjee, Dr. Partha Sharathi Dutta and Dr. Santanu Sarkar) core course for B.Tech. 2nd semester (January-May, 2024) Course handout
2. Advanced Partial Differential Equations (MA717) departmental elective for MSc and PhD stduents (January-May, 2024) Course handout
3. Mathematical Methods (MA512) core course for M.Sc. 3rd semester (August-December, 2023) Course handout
4. Applied Linear Algebra and Matrix Analysis (MA614) (Jointly with Dr. Sairam Kaliraj) departmental elective for B.Tech., MSc and PhD students (August-December, 2023)Course handout

Instructor (at IIT Jammu)

1. Linear Algebra and Differential Equations (jointly with Dr. Arvind Kumar), for B.Tech. second semester (March-July, 2023) Course handout
2. Analysis on Manifolds, Graduate level course, January-May, 2023 Course handout
3. Functional Analysis (jointly with Dr. Arvind Kumar), Graduate level course, January-May, 2023 Course handout
4. Probability and Statistics for M.Tech. students, August-December, 2022 Course handout
5. Introduction to Geometry and Geometric Analysis, Graduate level course, August-December, 2022 Course handout
6. Inverse Problems for linear hyperbolic PDEs, in an "Advanced Instructional School (AIS-IP) on Inverse Problems" held at TIFR CAM, Bengaluru, India, during July 4-23, 2022.
7. Linear Algebra and Applications, January-May, 2022 Course handout
8. Basic PDEs (jointly with Dr. Tanmay Sarkar), Graduate level course (January-May, 2022) Course handout
9. Functional Analysis and Applications, Graduate level course (September, 2021 to January, 2022) Course handout
10. Advanced Analysis, Graduate level course (September, 2021 to January, 2022) Course handout
11. Calculus (jointly with Dr. Rahul Kitture), for B.Tech. first semester (November, 2020 to March, 2021) Course handout

Teaching Assistant (at TIFR-CAM, Bangalore)

• Summer workout in Mathematics (SWIM) for undergraduate students, during June 21- July 15, 2018, organised by TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).
• Advanced instructional school (AIS) in linear partial differential equations (ATM School) , during July 3-8, 2017, at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant) (Video link) .
• Graduate course on functional analysis, during January-May, 2015 at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).
• Instructional School for Teachers (IST) on analysis and differential Equations (ATM School) , during December 7-19, 2015 at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).
• Graduate course on pde-2 (distribution theory and Sobolev spaces), during August-December, 2015, at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).
• Advanced Training in Mathematics School Workshop (ATMW) on partial differential equations of fractional order (ATM School) , during July 6-18, 2015 at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).
• Graduate course on differential geometry, during January-May, 2015 at TIFR Centre for Applicable Mathematics, Bangalore, India (Teaching assistant).

Students

PhD students

1. Rahul Bhardwaj; joined in March, 2021.
2. Mandeep Kumar; joined in September, 2021.
3. Parveen Kumar; joined in January, 2023.
4. Vinay Rana; joined in October, 2023.
5. Rajat; joined in January, 2024.

Masters students

• Nikhil Sharma, Cluster University of Jammu, India, August, 2022 to January, 2023. ( Thesis title: Three Fundamental Theorems in Metric Spaces)

Conferences

Conference/workshops