I am interested in differential geometry, geometric analysis, several complex variables, and mathematical physics. I dabble in other things (including applications) as they come my way. My PhD adviser was Leon A. Takhtajan.

• On Bott-Chern forms and their applications with Leon A. Takhtajan
  (Mathematische Annalen )
• On a generalised Monge-Ampere equation
  ( The Journal of Partial Differential Equations)
• A fully nonlinear PDE on a torus arising from Chern-Weil theory
  (The Electronic Journal of Differential Equations)
• Inverses of structured vector bundles with Indranil Biswas
  ( Geometriae Dedicata ).
• C^{2,a} estimates and existence results for certain nonconcave PDE
  (The Electronic Journal of Differential Equations)
• A priori estimates for a generalised Monge-Ampere PDE on some compact Kahler manifolds
  (Complex Variables and Elliptic equations )
• A note on the deformed Hermitian Yang-Mills PDE
  ( Complex Variables and Elliptic equations )
• Rational cuspidal curves on Del-Pezzo surfaces with Indranil Biswas, Shane D'Mello, and Ritwik Mukherjee.
  (The Journal of Singularities)
• A note on higher extremal metrics
  (Transactions of the American Mathematical Society)
• Representability of Chern-Weil forms
  (Mathematische Zeitschrift)
• Existence of coupled Kahler-Einstein metrics using the continuity method
  (International Journal of Mathematics )
• Metric properties of parabolic ample bundles with Indranil Biswas
  ( International Mathematics Research Notices )
• A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds with Indranil Biswas
  ( Epijournal de Geometrie Algebraique )
• A vector bundle version of the Monge-Ampere equation (The arxiv version has been corrected. The published version has a few minor errors.)
  (Advances in Mathematics)
• On coupled constant scalar curvature Kahler metrics with Ved Datar
  ( Journal of Symplectic Geometry)
• The deformed Hermitian Yang-Mills equation on three-folds
  (Analysis and PDE)
• A numerical criterion for generalised Monge-Ampere equations on projective manifolds with Ved Datar
  ( Geometric and Functional Analysis )
• A note on Demailly's approach towards a conjecture of Griffiths
  (Comptes Rendus - Mathematique)
• The Demailly system for a direct sum of ample line bundles on Riemann surfaces
  (Calculus of Variations and PDE)
• Criteria for the ampleness of certain vector bundles (with Indranil Biswas)
  (Proceedings of the American Mathematical Society)
• Positivity properties of the vector bundle Monge-Ampere equation (with Aashirwad N. Ballal)
  

• On the boundedness of effective potentials arising from string compactifications with M. Douglas and M. Disconzi
  (Communications in Mathematical Physics)
• On the Choquet-Bruhat-York-Friedrich formulation of the Einstein Euler equations with M. Disconzi
  (Modern Physics Letters A)
• Remarks on positive energy vacua via Effective potentials in String theory with S. Dabholkar and M. Disconzi
  (Letters in Mathematical Physics)
• Quillen metrics and perturbed equations
  (Letters in Mathematical Physics)
• Gravitating vortices and the Einstein-Bogomolnyi equations with Luis Alvarez-Consul, Mario Garcia-Fernandez, and Oscar Garcia-Prada.
  (Mathematische Annalen)
• Gravitating vortices with positive curvature with Mario Garcia-Fernandez, and Chengjian Yao.
  (Advances in Mathematics)
• Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface with Luis Alvarez-Consul, Mario Garcia-Fernandez, Oscar Garcia-Prada, and Chengjian Yao
  (Bulletin des Sciences Mathematiques).
  
• Non-abelian symmetric critical gravitating vortices on a sphere
  
• Gravitating vortices and Symplectic Reduction by Stages with Luis Alvarez-Consul, Mario Garcia-Fernandez, Oscar Garcia-Prada, and Chengjian Yao

• Bargmann-Fock extension from singular hypersurfaces with Dror Varolin
  (Crelle's Journal)
• On the asymptotics of the on-diagonal Szego kernel of certain Reinhardt domains with Arash Karami
  (Complex variables and Elliptic equations)
• Weighted interpolation from certain singular affine hypersurfaces
  (International journal of mathematics)
• Non-uniformly flat affine algebraic hypersurfaces with Dror Varolin
  (Nagoya Mathematical Journal. Erratum (with Arindam Mandal and Dror Varolin)).
• On an asymptotic characterisation of Griffiths semipositivity with Apoorva Khare.
  (Bulletin des Sciences Mathematiques)

• Computing Teichmuller maps between polygons with Mayank Goswami, David Gu, and Gaurish Telang
  (Presented at SoCG 2015 and appeared in the Journal of Foundations of Computational Mathematics).
• Load balanced short path routing in large-scale wirless networks using area-preserving maps with M. Goswami, C. Ni, D. Gu, and X.Ban
  (Proceedings of the 15th ACM international symposium on Mobile ad hoc networking and computing)
• Estimating a genius - Louis Nirenberg
  (Resonance)
• Stability of SGD : Tightness Analysis and Improved Bounds with Y. Zhang, W. Zhang, S. Bald, C. Chen, and M. Goswami
  (Accepted for poster presentation at UAI 2022)
• Physics helping mathematics: A couple of examples
  (Mathematics Student)