Projects per year
Personal profile
Research interests
I am a Lecturer (Assistant Professor) in Mathematics. My original background was in Computer Science, where I spent 10 years (including experience in the industry), before moving to the world of Mathematics. My research interests have broadly evolved at the intersection of these two fields.
My current interests lie at the intersection of Computational Methods, Numerical Analysis and Quantum Mechanics.
Current Interests:
Numerical Methods for Evolutionary Equations (PDEs, ODEs, SDEs), Simulation of Quantum Systems (Spins, NMR, Atomic & Molecular Systems), Optimal Control and Design, Convergence Analysis.
Techniques:
Splitting and Composition Methods, Krylov Subspace Methods, Deep Learning, Numerical Optimization, Lie Group Methods, Geometric Numerical Integration
Applications:
Quantum Computing, Nuclear Magnetic Resonance (NMR/MRI), Laser matter interaction, Fibre optics, Photovoltaic cells.
Previous interests:
Proof Systems and Formal Verification, Programming Language Design, Geometric Computer Vision.
For more details, please visit my personal website.
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
Education/Academic qualification
Applied Mathematics, Doctor of Philosophy, High accuracy computational methods for the semiclassical Schrödinger equation, University of Cambridge
17 Jan 2012 → 30 Sept 2016
Award Date: 28 Apr 2018
Applied Mathematics, Master of Advanced Studies (MASt or Part III), University of Cambridge
1 Oct 2008 → 30 Jun 2009
Computer Science and Engineering, BTech & MTech, Indian Institute of Technology Kanpur
1 Jul 2000 → 30 Jun 2005
External positions
Junior Research Fellow in Mathematics, University of Oxford
1 Oct 2016 → 1 Sept 2019
Keywords
- Numerical Analysis
- PDEs
- Quantum Mechanics
- Optimal Control
- Deep Learning
- Krylov Subspace Methods
- Geometric Numerical Integration
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Collaborations and top research areas from the last five years
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LMS Grant Scheme 5 - Quantum Complexity and Verification
Singh, P. (PI)
28/01/24 → 31/07/26
Project: UK charity
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HIMR Small Grant - Computational Mathematics for Quantum Technologies Workshop
Singh, P. (PI)
Heilbronn Institute for Mathematical Research
1/08/22 → 6/08/22
Project: UK charity
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ICMS Strategic Workshop - Advances in N-body Computations, Oxford
Singh, P. (PI)
5/04/22 → 4/05/22
Project: UK charity
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LMS Scheme 6 - Advances in N body Computations Workshop, Oxford
Singh, P. (PI)
16/03/22 → 30/04/22
Project: UK charity
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Fine Tuning Numerical Schemes for PDEs
Frasca-Caccia, G. & Singh, P., 7 Jun 2024, AIP Conference Proceedings. Simos, T. E. & Tsitouras, C. (eds.). American Institute of Physics, 4 p. 220007. (AIP Conference Proceedings; vol. 3094, no. 1).Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding
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Learning efficient and provably convergent splitting methods
Kreusser, L. M., Lockyer, H. E., Müller, E. H. & Singh, P., 14 Nov 2024.Research output: Working paper / Preprint › Preprint
File28 Downloads (Pure) -
Optimal parameters for numerical solvers of PDEs
Frasca-Caccia, G. & Singh, P., 31 Oct 2023, In: Journal of Scientific Computing. 97, 1, 11.Research output: Contribution to journal › Article › peer-review
Open Access1 Citation (SciVal) -
Quantum simulation of highly-oscillatory many-body Hamiltonians for near-term devices
Chen, G., Foroozandeh, M., Budd, C. & Singh, P., 13 Dec 2023, (Submitted) arXiv.Research output: Working paper / Preprint › Preprint
File29 Downloads (Pure) -
Unitarity of some barycentric rational approximants
Jawecki, T. & Singh, P., 23 Aug 2023, In: IMA Journal of Numerical Analysis.Research output: Contribution to journal › Article › peer-review
Open AccessFile1 Citation (SciVal)26 Downloads (Pure)