Pranav Singh
Junior Research Fellow in Mathematics

Profile

I am a Junior Research Fellow in Mathematics at Trinity College, Oxford.
I am an applied mathematician, specialising in computational mathematics. I have an undergraduate and Masters degrees in Computer Science from IIT Delhi and a Part III in Mathematics from Cambridge. I did my doctoral research in Applied Mathematics at Cambridge, funded by a King’s College Studentship.

Research

My research interests are in the field of computational mathematics, in particular the numerical solution of partial differential equations (PDEs) arising in the physical sciences.
I am currently interested in investigating numerical methods for quantum systems described by a range of equations such as the linear, nonlinear and stochastic versions of the Schrödinger equation, and related equations such as the Pauli, Dirac and Klein–Gordon equations.
I am interested in Lie algebraic techniques such as the Magnus expansion and Zassenhaus splittings, whose combination is very effective for the simulation of equations with time-varying fields and holds great promise for control of quantum systems.

Selected Publications

 Bader, P., Iserles, A., Kropielnicka, K. and Singh, P., “Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential”, forthcoming in Proc. Roy. Soc. A.
 Singh, P., “Algebraic theory for higher-order methods in computational quantum mechanics”, arXiv:1510.06896 [math.NA], 2015.
 Bader, P., Iserles, A., Kropielnicka, K. and Singh, P., “Effective approximation for the linear time-dependent Schrödinger equation”, Found. Comp. Maths 14 (2014), 689-720.