About Me

I am a faculty member in mathematics department at Indian Institute of Technology (IIT-JMU) Jammu, India.

My research interests are:

  • Inverse problems related to PDEs
  • Geometric inverse problems
  • Integral geometry
  • Inverse scattering problems
  • Partial differential equations

Work Experience

  • September 2020 to present : Assistant Professor in the department of mathematics (Maths) at Indian Institute of Technology (IIT-JMU) Jammu, India.
  • Dec 2018 to June, 2020 : Post-doctoral fellow in the division of Applied and Computational Mathematics (ACM) of Beijing Computational Science Research Center (CSRC) Beijing, China.
    Mentor : Professor Guang-Hui Hu
  • Aug-Nov, 2018 : Post-doctoral fellow at
    Tata Institute of Fundamental Research (TIFR) Centre for Applicable Mathematics (CAM) Bangalore, India
    Mentor : Professor Venkateswaran P. Krishnan

Education

  • Aug 2015 to July 2018 : Doctor of Philosophy (Ph.D.) in Mathematics from
    Tata Institute of Fundamental Research (TIFR) Centre for Applicable Mathematics (CAM) Bangalore, India
    Advisor : Professor Venkateswaran P. Krishnan
    Thesis Title: Some inverse problems in hyperbolic partial differential equations, defended on July 13, 2018; (PDF).
  • Aug 2014 to July 2015 : Master of Philosophy (M.Phil.) in Mathematics from
    Tata Institute of Fundamental Research (TIFR) Centre for Applicable Mathematics (CAM) Bangalore, India
    Advisor : Professor Venkateswaran P. Krishnan
    Thesis title : Inverse problems related to hyperbolic partial differential equations and hybrid imaging.
  • July 2012 to July 2014 : Master of Science (M.Sc.) in Mathematics from
    Tata Institute of Fundamental Research (TIFR) Centre for Applicable Mathematics (CAM) Bangalore, India
    Courses studied.
  • July 2009 to July 2012 : Bachelor of Science (B.Sc.) honours in Mathematics from
    Pt. Neki Ram Sharma (NRS) Govt. College, Rohtak, affiliated to
    Maharshi Dayanand University (MDU), Rohtak, Haryana, India
    Courses studied.

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Research

Preprints

  1. Gen Nakamura, Manmohan Vashisth and Michiyuki Watanabe; Inverse Initial Boundary Value Problem for a Non-linear Hyperbolic Partial Differential Equation, Submitted (arXiv).
  2. Guang-Hui Hu, Manmohan Vashisth and Jiaqing Yang; Inverse time-harmonic electromagnetic scattering from coated polyhedral scatterers with a single far-field pattern, Submitted (arXiv).
  3. Ibtissem Ben Aïcha, Guang-Hui Hu, Manmohan Vashisth and Jun Zou; Uniqueness for time-dependent inverse problems with single dynamical data, Submitted (arXiv).
  4. Manmohan Vashisth; Unique determination of the damping coefficient in the wave equation using point source and receiver data, Submitted (arXiv).

Publications

  1. Guang-Hui Hu and Manmohan Vashisth; Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave, Inverse Problems, (IP-2020). (PDF).
  2. 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).
  3. Rohit Kumar Mishra and Manmohan Vashisth; Determining the time dependent matrix potential appearing in a wave equation from partial boundary data, Applicable Analysis (AA-2020) (PDF).
  4. 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).
  5. 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).
  6. 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).
  7. Venkateswaran P. Krishnan and Manmohan Vashisth; An inverse problem for the relativistic Schroedinger equation with partial boundary data, Applicable Analysis, Volume 99, No. 11, 1889-1909. (AA-2019) (PDF).

Collaborators

  1. Ibtissem Ben Aïcha (Beijing Computational Sciecne Research Center, Beijing, China)
  2. Cătălin I. Cârstea (Sichuan University, Sichuan, China)
  3. Guang-Hui Hu (Beijing Computational Sciecne Research Center, Beijing, China)
  4. Venkateswaran P Krishnan (TIFR Centre for Applicable Mathematics, Bengaluru, India)
  5. Rohit Kumar Mishra (University of texas at Arlington, USA)
  6. Gen Nakamura (Hokkaido University, Sapporo, Japan)
  7. Suman Kumar Sahoo (TIFR Centre for Applicable Mathematics, Bengaluru, India)
  8. Soumen Senapati (TIFR Centre for Applicable Mathematics, Bengaluru, India)
  9. Jiaqing Yang (Xi'an Jiaotong University, Xi'an, China)
  10. Michiyuki Watanabe (Okayama University of Science, Japan)
  11. Jun Zou (The Chinese University of Hong Kong, Hong Kong)

Academic Visits

Talks

  1. 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).
  2. 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).
  3. TIFR Centre Applicable Mathematics, (CAM) Bengaluru, India, on February 14, 2020. (Talk title : A partial data inverse problem for the Convection-diffusion equation).
  4. 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).
  5. 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).
  6. 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).
  7. 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).
  8. The 9th International Conference on Inverse Problems and Related Topics (ICIP-2018) during Aug 13-17, 2018, Singapore, organised by National University of Singapore (NUS). (Talk title: Inverse boundary value problems for non-linear hyperbolic PDE).
  9. Beijing Computational Science Research Center (CSRC), Beijing, China on Feb 7, 2018. (Talk title : A partial data inverse problem for the Covection-diffucion equation).
  10. 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).
  11. Hokkaido University, Sapporo, Japan (HOKUDAI) on June 16, 2017. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
  12. 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).
  13. International Conference of The Indian Mathematics Consortium (TIMC) in cooperation with American Mathematical Society (AMS) (BHU-2016) during Dec 13-17, 2016, BHU-Varanasi, India. (Talk title : Determination of time-dependent coefficients for a hyperbolic inverse problem from partial data).
  14. International conference on Mathematical Analysis and its Applications (ICMAA-2016) during Nov 28 - Dec 2, 2016, IIT-Roorkee, India. (Talk Title : Inverse Problems for Wave Equation in 3-D with Under-determined Data).
  15. 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).
  16. 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).
  17. In-house symposium Talk on Aug 5, 2015 in TIFR Centre for Applicable Mathematics, Bangalore, India. (Talk Title : Inverse Problems in Hybrid Imaging).

Teaching

CV

Contact

manmohan.vashisth@iitjammu.ac.in
manmohanvashisth@gmail.com

Manmohan Vashisth
Assistant Professor
Deapartment of Mathematics
Indian Institute of Technology, Jammu Jagti
Nagrota Bypass Road, Jammu & Kashmir
181221, India

+91-191-274-1154