Saikat Mazumdar

Research Interests

• Nonlinear partial differential equations
• Nonlinear Analysis on Manifolds
• Geometric Analysis

Preprints

• Sharp quantitative stability of Struwe’s decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space: Part I, with M. Bhakta, D. Ganguly, D. Karmakar. (2023) arXiv:2211.14618 .

• Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows, with M. Bhakta, D. Ganguly, D. Karmakar. (2022) arXiv:2207.11024.

Publications 

• Existence result for the higher-order Q–curvature equation, with J. Vétois. Calc. Var. Partial Differential Equations (to appear) arXiv:2007.10180.

• Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up, with D. Ganguly and D. Karmakar. Adv. Differential Equations. 28 (2023), no. 9-10, 779−805. arXiv:2201.02400.

• Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds, with J. Flynn, N. Lam, G. Lu. Journal of Geometric Analysis 33 (2023), no.1, Paper No. 27, 34 pp . arXiv:2103.12788.

• Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold, with J. Vétois. Discrete Contin. Dyn. Syst. 42 (2022), no.11, 5273–5287. arXiv:2106.12256.

• The Hardy–Schrödinger Operator on the Poincaré Ball: Compactness and Multiplicity, with N. Ghoussoub and F. Robert. J. Differential Equations, 320 (2022), 510−557. arXiv:1804.05991.

• Multiplicity and stability of the Pohozaev obstruction for Hardy-Schrödinger equations with boundary singularity, with N. Ghoussoub and F. Robert. Memoirs of the Amer. Math. Soc. 285 (2023), no.1415. arXiv:1904.00087.

• Mass and Extremals Associated with the Hardy-Schrödinger Operator on Hyperbolic Space, with H. Chan, N. Ghoussoub, S. Shakerian, L. Faria. Adv. Nonlinear Stud. 18 (2018), no. 4, 671−689. arXiv:1710.01271.

• Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy. Nonlinear Analysis, 169 (2018), 190-217. arXiv:1702.03480

• Struwe's Decomposition  for a Polyharmonic Operator on a Compact Riemannian Manifold with or without boundary. Commun. Pure Appl. Anal. 16 (2017), no. 1, 311–330. arXiv:1603.07953.

• GJMS-type Operators on a compact Riemannian manifold: Best constants and Coron-type solutions. J. Differential Equations, 261 (2016), no. 9, 4997-5034. arXiv:1512.0212

Teaching

      IIT Bombay

• MA 417 :    Ordinary Differential Equations
• MA 5106 :  Introduction to Fourier Analysis
• MA 534 :    Modern Theory of PDEs
• MA 205 :    Complex Analysis
• MA 581 :    Elements of Differential Topology
• MA 817 :    Partial Differential Equations I
• MA 214 :    Introduction to Numerical Analysis
• SI 416   :    Optimization
• SI 507   :    Numerical Analysis

IIT Bombay Geometric Analysis Seminar