Publications / Prépublications - Preprints

Prépublications / Preprints

• Z-critical equations for holomorphic vector bundles on Kähler surfaces (2024) with C. Scarpa [Arxiv]
• Quantization of Hitchin's equations for Higgs bundles I (2016), with M. Garcia-Fernandez and J. Ross [Arxiv]

Publications (see my collaborators here)

• A variational approach to the Hermitian-Einstein metrics and the Quot-scheme limit of Fubini-Study metrics (2019), with Y. Hashimoto, Geometriae Dedicata, 219, 50 (2025)
• Quot-scheme limit of Fubini-Study metrics and its applications to balanced metrics, with Y. Hashimoto, in Birational Geometry, Kähler–Einstein Metrics and Degenerations, Springer Proceedings in Mathematics & Statistics (2023)
  
• Quot-scheme limit of Fubin-Study metrics and Donaldson's functional for vector bundles, with Y. Hashimoto, Epijournal de Géométrie Algébrique, volume 5 (2022), article no. 21 
• On the lower bounds of the L2-norm of the Hermitian scalar curvature (2017),  with M. Lejmi, Journal of Symplectic Geometry, 18, no 2, 537--558 (2020) [Arxiv|Int. Press]
• Relative K-polystability of projective bundles over a curve, with V. Apostolov, Trans. Amer. Math. Soc, 372 no. 1, 233--266 (2019) [Arxiv|AMS]
• Construction of constant scalar curvature Kähler cone metrics, with K. Zheng,  Proc. London Math. Soc. 117, no 3, 527-573 (2018)  [Arxiv|LMS]
• About J-flow, J-balanced metrics, uniform J-stability and K-stability (2017), with Y. Hashimoto, Asian J. Math 22 no.3 391-412, special issue dedicated to Prof. N. Mok's 60th birthday (2018) [Arxiv|Int. Press]
• A finite dimensional approach to Donaldson's J-flow, with R. Dervan, to appear in Comm. Anal. Geom 62 pages (2017) [Arxiv].
• Quantization of the Laplacian operator on vector bundles, I    with J. Meyer and R. Seyyedali, Math Annalen (2015) 43 pages (DOI: 10.1007/s00208-015-1355-0) [ArXiv|Springer]
• About canonical Kähler metrics on Mumford semistable projective bundles over a curve, Journal of the London Mathematical Society 93 (1): 159-174 (2016)  (DOI : 10.1112/jlms/jdv066) [ArXiv|Oxford Journals]
• Quantization of Donaldson's heat flow over projective manifolds with R. Seyyedali, Math. Zeitschrift (DOI: 10.1007/s00209-015-1567-8) (2015) 28 pages [Arxiv|Springer]
• Numerical Weil-Petersson metrics on moduli space of Calabi-Yau manifolds, with S. Lukic, Journal of Geometry and Physics (2015), doi:10.1016/j.geomphys.2015.02.018  [ArXiv|Sciencedirect]
• Some remarks about Chow, Hilbert and K-stability of ruled threefolds, Contribution to 9th ISAAC congress 2013, Birkhäuser Trends in Math. series (2014) [Springer|PDF]
• Geometric quantization of complex Monge-Ampère Operator for certain diffusion flows, Lecture Notes in Computer Science 8085, Springer-Verlag, 612-621 (2013) [PDF|Springer]. Here are slides.
• Balancing Kähler flow for the Calabi problem, with H.D. Cao, Journal of European Math. Soc., 15 no.3, 1033-1067 (2013) [ArXiv|EMS]
• A note on Chow stability of the Projectivisation of Gieseker Stable Bundles, with J. Ross, Journal of Geom. Analysis (2012) (DOI: 10.1007/s12220-012-9384-3)  [ArXiv|Springer]
• A non trivial example of coupled equations for Kähler metrics and Yang-Mills connections, with Christina W. Tonnesen-Friedman, Central European Journal of Math., 10(5), 1673-1687 (2012) [ArXiv|Springer]
• About Bergman geodesics and homogenous complex Monge-Ampère equations, with R. Berman, Lecture Notes in Mathematics 2038, Springer, 283--302 (2012) [PDF|Springer]
• About Kähler quantization and the Calabi Problem, Acta Physica Polonica B. Vol 4  no. 3, 325-340 (2011) [ActaPhys|PDF]
• Twisted balanced metrics. In "Lie Groups :  New research",  Mathematics Research Developments , Editor Altos B. Canterra, 267--281, Novapublishers NJ, ISBN 978-1606923894 (2009) [PDF] 
• Ricci iterations on Kähler classes, J. Inst. Math. Jussieu 8, no. 4, 743--768 (2009) [ArXiv|JIMJ]. [Previous] version of this work.
• Canonical metrics for Vortex type equations. Math. Annalen, no 337, 923-979 (2007). [ArXiv|Math Annalen]
• Canonical metrics and Härder-Narasimhan filtration. Contemporary aspects of complex analysis, differential geometry and mathematical physics, 132-148, World Sci. Publ., Hackensack, NJ (2006)  [WorldSci|PDF]
• Oberwolfach Reports no. 32 (2007)  and no. 39 (2010)

Numerical computations

Thèses

Preprints in preparation

Old preprints not submitted

Papers intended for a large public