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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.Here is my CV .

PhD and Int-PhD students :

List of publications and preprints:

Differential geometry and geometric analysis :

- 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*)

- 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

- 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*)