Ratnakumar P K – Director
📧 ratnapk@ksom.res.in
📞 0495 2809001
Office: Director's Office
Prof. P. K. Ratnakumar is the Director of the Kerala School of Mathematics. He is a leading expert in harmonic analysis and partial differential equations, with a particular focus on the analysis of the Heisenberg group and the twisted Laplacian on complex spaces.
His research encompasses Schrödinger equations, modulation spaces, Hermite operators, Fourier analysis, and analytic aspects of function spaces. Prof. Ratnakumar's extensive collaborations include work on bilinear estimates, convolution operators, and regularity results for Fourier integral operators.
Selected Recent and Impactful Publications
- Non-isometric translation and modulation invariant Hilbert spaces (with J. Toft and J. Vindas), J. Math. Anal. Appl., 2025.
- Fourier multipliers via twisted convolution (with A. K. Maity), Proc. Amer. Math. Soc., 2025.
- Young's inequality for the twisted convolution , J. Fourier Anal. Appl., 2023.
- Functions operating on modulation spaces and nonlinear dispersive equations (with D. G. Bhimani), J. Funct. Anal., 2016.
- Nonlinear Schrödinger equation and the twisted Laplacian—global well posedness (with V. K. Sohani), Math. Z., 2015.
- Schrödinger equation and the oscillatory semigroup for the Hermite operator (with A. K. Nandakumaran), J. Funct. Anal., 2005.