NISER

• Ph. D., 2017, Harish-Chandra Research Institute, Advisor: Prof. P. K. Ratnakumar
• M. Sc., 2010, Indian Institute of Technology Madras
• B. Sc., 2008, Midnapore college

Harmonic Analysis

• DST INSPIRE Faculty Fellowship, 2020
• C.V. Raman Fellowship, IISc, 2020
• Dr. D. S. Kothari Fellowship, 2019
• National Post Doctoral Fellowship (N-PDF) - SERB, 2017 - 2019
• NBHM postdoctoral fellowship, 2017 (did not avail)
• Masters Scholarships-2009, NBHM, Dept. of Atomic Energy, Govt. of India, India

Published in Journals / Selected publications:

• Nonlinear operations and Factorizations on a class of affine modulation spaces, M. H. A. Biswas and R. Manna,  Forum Mathematicum, To appear.
• Pseudo-differential Operators and Weyl Transform on Gr\'elaud's Group, R. Manna, S. K. Nayak,  Israel Journal of Mathematics, To appear.
• Revisit on Heisenberg uniqueness pair for the hyperbola, D. Giri, R. Manna, Math. Z. 306 (2024), no. 3, 15 pp.
• On heat equations associated with fractional harmonic oscillators, D. G. Bhimani, R.  Manna, F.  Nicola, S. Thangavelu, S. I. Trapasso, Fract. Calc. Appl. Anal. 26 (2023), no. 6, 2470–2492.
• Revisit of multi-dimensional Bohr radius, S. Kumar, R. Manna, J. Math. Anal. Appl. 523 (2023), no. 1, 15 pp.
• Fractional Fourier transforms, harmonic oscillator propagators and Strichartz estimates on Pilipović and modulation spaces, J. Toft, D. G. Bhimani, R.  Manna, Appl. Comput. Harmon. Anal. 67 (2023), 38 pp.
• Trace mappings on quasi-Banach modulation spaces and applications to pseudo-differential operators of amplitude type, J. Toft, D. G. Bhimani, R.  Manna, Anal. Appl. (Singap.) 21 (2023), no. 2, 453–495.
• An extension problem, trace Hardy and Hardy's inequalities for Ornstein-Uhlenbeck operator, P. Ganguly, R. Manna, S. Thangavelu, Analysis & PDE, Anal. PDE 16 (2023), no. 5, 1205–1244.
• Global Fourier integral operators in the plane and the square function, R. Manna, P. K.  Ratnakumar,  J. Fourier Anal. Appl. 28 (2022), no. 2, Paper No. 25, 28 pp.
•  Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness, D. G. Bhimani, R.  Manna, F.  Nicola, S. Thangavelu, S. I. Trapasso,  Adv. Math. 392 (2021), 18 pp.
•  On a theorem of Chernoff on rank one Riemannian symmetric spaces, P. Ganguly, R. Manna, S. Thangavelu J. Funct. Anal. 282 (2022), no. 5, Paper No. 109351, 31 pp.
•  On the existence of global solutions of the Hartree equation for initial data in the modulation space Mp,q(R), Ramesh Manna, J. Differential Equations 317 (2022), 70–88.
•  Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation, Agnid Banerjee, Ramesh Manna, Discrete Contin. Dyn. Syst. 41 (2021), no. 11, 5105–5139. 
•  A Strong Unique Continuation Property for the Heat Operator with Hardy Type Potential,  Agnid Banerjee, Nicola Garofalo and  Ramesh Manna,  J Geom Anal (2021), https://doi.org/10.1007/s12220-020-00487-y.
•  Space like strong unique continuation for sublinear parabolic equations,  Agnid Banerjee, Ramesh Manna,  Journal of the London Mathematical Society, 102 (2020), no. 1, p. 205-228.
•  Translation and modulation invariant Hilbert spaces, J. Toft,  A.  Gumber, R. Manna, P. K.  Ratnakumar,  Monatsh. Math. 196 (2021), no. 2, 389–398.
•  Borderline gradient estimates at the boundary in Carnot groups,  Ramesh Manna, Ram Baran Verma, Proc. Roy. Soc. Edinburgh Sect. A 151 (2021), no. 6, 1920–1953.
•  Momentum Ray Transforms, II: Range Characterization In the Schwartz space},  V. P. Krishnan, R. Manna, S. K. Sahoo, V. Sharafutdinov,  Inverse Problems, 36 (2020), no. 4, 045009, 33 pp.,  arXiv:1909.07682
•  Carleman estimates for Baouendi-Grushin operators with applications to quantitative uniqueness and strong unique continuation,  Agnid Banerjee,  Nicola Garofalo, Ramesh Manna,  Applicable Analysis,  Appl. Anal. 101 (2022), no. 10, 3667–3688.
•  Local smoothing of Fourier integral operators and Hermite functions,  Ramesh Manna,  P. K. Ratnakumar,  Special ISAAC volume "Advances in Harmonic Analysis and Partial Differential Equations", DOI: https://doi.org/10.1007/978-3-030-58215-9_1.
•  Maximal functions associated to flat plane curves with Mitigating factors,  Ramesh Manna, Annali di Matematica Pura ed Applicata (1923 -)(4), vol. 198 (2019), no. 1, 143-156.
•  Weighted estimates for maximal functions associated with finite type curves in R^2,  Ramesh Manna, Saurabh Shrivastava and Kalachand Shuin, Nonlinear Analysis, 205 (2021), 112225, 24 pp.
•  Maximal functions along Hypersurfaces,  Ramesh Manna, P. K. Ratnakumar, Journal of the Ramanujan Mathematical Society, vol. 33., no. 3  (2018), pp. 283-296.
•  The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces,  Ramesh Manna, Journal of Fourier Analysis and Applications, vol.  25, (2019), no. 4, 1319-1349.
•  Modulation spaces and non-linear Hartree type equations,  Ramesh Manna, Nonlinear Analysis, 162 (2017), pp. 76--90.
• Momentum ray transforms ,  V. P. Krishnan, R. Manna, S. K. Sahoo, V. Sharafutdinov,  Inverse Problems and Imaging, 2019, vol. 13(3): 679-701 doi: 10.3934/ipi.2019031.

Harmonic Analysis

• M306- Calculus of several variables (Fall-2021), NISER
• M301- Lebesgue Integration (Spring-2022), NISER
• M306 & MA705- Calculus of several variables (Fall-2022), NISER
• MA607 & M451-(Advanced) Complex Analysis, (Spring-2023), NISER
• MA605-Topology 1, (Fall-2023), NISER
• M555 & MA882- Harmonic Analysis, (Spring-2024), NISER

• UGCS Convener (2022-)
• Member, Mathematics Colloquium/Seminar Coordination, SMS (2022-)