Welcome!

I'm Dr. Mansi Singh, currently a Postdoctoral Researcher in the Department of Applied Mathematics at the Mathematical Institute for Machine Learning and Data Science (MIDS), Katholische Universität Eichstätt-Ingolstadt (KU), Germany (January 2025–Present). My position is funded through the DFG Collaborative Research Centre Transregio TRR 181, "Energy Transfers in Atmosphere and Ocean". I'm a member of the Subproject M3, "Towards Consistent Subgrid Momentum Closures", under the supervision of Prof. Marcel Oliver, I investigate fundamental mathematical questions related to multiscale energy transfer, hydrodynamic instabilities, and reduced-order modelling in geophysical fluid dynamics, with applications to atmosphere–ocean systems.

Prior to joining KU, I worked as a Postdoctoral Fellow in the Department of Applied Mechanics at the Indian Institute of Technology (IIT) Madras (September 2024–December 2024) under the supervision of Prof. Anubhab Roy. My research spanned hydrodynamic instabilities, internal gravity waves, and Stokes flows, with an emphasis on rigorous mathematical analysis. 

I obtained my PhD from the Department of Mathematics, Indian Institute of Technology (IIT) Kharagpur, India, under the supervision of Dr. Rupanwita Gayen. My doctoral research was centred on the mathematical modelling of surface gravity wave–structure interactions. During my PhD, I was supported by the prestigious Prime Minister's Research Fellowship, awarded by the Government of India (January 2021–July 2024). 

In short, my research focuses on the mathematical modelling of wave–structure interactions, hydroelasticity, hydrodynamic instabilities, and multiscale energy transfer in geophysical flows. Using integral equations, Green’s functions, complex variable techniques, asymptotic analysis, spectral methods, and stability theory, I develop analytical and computational frameworks to investigate nonlinear wave dynamics, fluid–structure interactions, perturbation growth, and energy cascade processes in oceanic and atmospheric systems.