Projects in progress
Higher dimensional Brill-Noether theory in terms of L infinity pairs, in collaboration with N. Budur.
Theory of equivariant deformations of isolated singularities, in collaboration with Sasha Viktorova.
Theory of analytic stacks and their local structure, in collaboration with Laurent Meersseman.
Publications & Preprints
Brill-Noether theory for surfaces (with N. Budur). In preparation.
Deformations with cohomology constraints (with N. Budur). arXiv (2023). To appear in Panoramas et Synthèses, SMF (2025).
Local structure of the Teichmüller and the Riemann moduli stacks. arXiv (2023). Collectanea Mathematica (2024), Journal link.
Formal moduli problems with cohomological constraints. arXiv (2022). To appear in Communications in Algebra (2025).
Group actions on local moduli space of holomorphic vector bundles. arXiv (2022). Canadian Mathematical Bulletin (2022), Journal link.
A note on the group extension problem to semi-universal deformation. arXiv (2021). Indagationes Mathematicae (2023), Journal link.
Semi-prorepresentability of formal moduli problems and equivariant structures. arXiv (2021). Homology, Homotopy and Applications (2024), Journal link.
Equivariant Kuranishi family of compact complex manifolds. arXiv (2020). Manuscripta Mathematica (2021), Journal link.
A counter-example to the equivariance structure on semi-universal deformation. arXiv (2019). Journal of Geometric Analysis (2020), Journal link.
Invited talks
“Of moduli and their special loci”. IASM - Harbin Institute of Technology, April 2025.
“Brill-Noether theory on curves in terms of L-infinity pairs”. Seminar Algebra-Geometry-Topology, VNU-HUS, Hanoi, January 2025.
“Brill-Noether theory on curves in terms of L-infinity pairs”. Séminare ALPE, IMAG, Montpellier, December 2024.
“Théorie de Brill-Noether sur des courbes en termes de L-infinies paires”. Séminaire systèmes dynamiques et géométrie, LAREMA, Angers, November 2024.
"Local structure of analytic stacks". Seminar Number Theory and Algebraic Geometry, KU Leuven, Belgium, February, 2024.
"Sur la structure locale des champs analytiques". Séminaire de Géométrie complexe, Institut Élie Cartan, Nancy, January 2024.
"Sur la structure locale des champs analytiques". Séminaire Géométries, Institut Camille Jordan, Lyon, November 2023.
"Introduction to (derived) deformation theories". Seminar Geometry and Topology, VAST, Vietnam, March - May 2023.
"The Riemann moduli stack and its local structure". Conference: Singularities and Algebraic Geometry, Nha Trang, Vietnam, February 2023.
"Champs de Riemann et leur structure locale". Séminaire de Géométrie & Topologie, LMBA, Brest, France, November 2022
"Sur une question de Rydh". Journée de rentrée, CMLS, Palaiseau, September 2022.
“Equivariant Kuranishi family of complex compact manifolds”. Séminaire systèmes dynamiques et géométrie, LAREMA, Angers, May 2022.
“Of (formal) moduli problems and equivariant structures”. Seminar: Algebra & Geometry, Royal Institute of Technology, Sweden, March 2022.
“Déformations dérivées équivariantes de variétés algébriques”. Journée de fin d'année, IMJ-PRG, Paris, July 2021.
“Equivariance structures on semi-universal deformations”. Thematic month: Complex Geometry, CIRM, Marseille, January 2019.
Referee
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg,
Journal of Differential Geometry.
Some notes
Learning note on D-modules and its applications. pdf
A detailed explanation of Bogolomov's paper: On the Cohomology Ring of a Simple Hyperkähler Manifold. pdf
Deformations of complex structures. pdf
A gentle introduction to Singular homology and its applications. pdf
Polynomial representations of the general linear group - Undergraduate thesis supervised by Prof. Le Minh Ha. pdf
Ph.D thesis: pdf. The reader is warmly referred to reviewed papers [1] , [2], [3] and [4] corresponding to the chapters therein, for more precision.
