
Designation
Assistant Professor
Joining Date
Research Area
Harmonic Analysis
Education
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
Research Interest
Harmonic Analysis
Awards
• 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
Publications
Published in Journals / Selected publications:
- An extension problem, trace Hardy and Hardy's inequalities for Ornstein-Uhlenbeck operator, P. Ganguly, R. Manna, S. Thangavelu, Analysis & PDE, To Appear.
- 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, DOI: https://doi.org/10.1017/prm.2020.86.
- 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.
Teaching
- 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
Sponsored Projects
- DST INSPIRE 2021 - 2025