• Differential geometry : canonical Kähler metrics, perturbative techniques, moment maps.

• Complex algebraic geometry : K-stability, slope stability, GIT, deformation theory, toric varieties.

• Mathematical physics : Yang-Mills connections, Calabi-Yau varieties, Hull-Strominger system.

Research Papers

1. "Foldable fans, cscK surfaces and local K-moduli",
   ArXiv 2402.01159


2. "Toric sheaves and flips",
   with Andrew Clarke and Achim Napame. ArXiv 2309.09267


3. "On the Futaki invariant of Fano threefolds",
   with Lars Martin Sektnan, Annali dell'università di Ferrara (2024). Journal.
   ArXiv 2307.02258


4. "Semi-stability and local wall-crossing for hermitian Yang-Mills connections",
   with Andrew Clarke, to appear in Journal of Symplectic Geometry (2024). Journal.
   ArXiv 2304.05245


5. "A note on stable toric sheaves of low rank",
   Arxiv 2307.02822


6. "Blowing-up Hermitian Yang--Mills connections",
   with Andrew Clarke. ArXiv 2301.00525


7. "Analytic K-semistability and wall-crossing",
   with Lars Martin Sektnan. ArXiv 2212.08383


8. "Toric sheaves, stability and fibrations",
   with Achim Napame, J. Pure Appl. Algebra 228, No. 3, Article ID 107494, 30 p. (2024). Journal.
   ArXiv 2210.04587


9. "Hermitian Yang-Mills connections on pullback bundles",
   with Lars Martin Sektnan, Calc. Var. Partial Differ. Equ. 63, Paper No. 13, 63p. (2024). Journal.
   ArXiv 2006.06453


10. "T-dual solutions and infinitesimal moduli of the G2-Strominger system",
    with A. Clarke and M. Garcia-Fernandez, Adv. Theor. Math. Phys., vol.26, no.6, 1669-1704, 2022. Journal.
    ArXiv 2005.09977


11. "The Zariski-Lipman conjecture for toric varieties",
    J. Algebra, 609 (2022), pp. 547-551. Journal.
    ArXiv 2202.02109


12. "Gauge theory for string algebroids",
    with Mario Garcia-Fernandez and Roberto Rubio, to appear in Journal of Differential Geometry. Journal.
    ArXiv 2004.11399


13. "Canonical metrics on holomorphic Courant algebroids",
    with M. Garcia-Fernandez, R. Rubio and C. Shahbazi, Proc. London Math. Soc., 125: 700-758 (2022). Journal.
    ArXiv 1803.01873


14. "Equivariant stable sheaves and toric GIT",
    with Andrew Clarke, Proc. R. Soc. Edinb., Sect. A, Math., 153(2), 385-416 (2023). Journal.
    ArXiv 2001.01500


15. "Relative Chow stability and optimal weights",
    Proc. Amer. Math. Soc., vol. 151, no. 9 (2023), 4015-4026. Journal.
    ArXiv 1710.02536


16. "A moment map picture of relative balanced metrics on extremal Kähler manifolds",
    with Yuji Sano, J. Geom. Anal. 31 (2021), 5941-5973. Journal.
    ArXiv 1703.09458


17. "Holomorphic string algebroids",
    with Mario Garcia-Fernandez and Roberto Rubio, Trans. Amer. Math. Soc. 373 (2020), 7347-7382. Journal.
    ArXiv 1807.10329


18. "The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics",
    with Roberto Rubio, Rev. Mat. Iberoam. 36 (2020), 485--536. Journal.
    ArXiv 1612.03755


19. "Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry"
    with Mario Garcia-Fernandez and Roberto Rubio, Math. Ann. (2017) 369: 539--595. Journal.
    ArXiv 1503.07562


20. "Extremal metrics and lower bound of the modified K-energy"
    with Yuji Sano, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 9, 2289-2310. Journal.
    ArXiv 1211.5585


21. "Deformations of constant scalar curvature Sasakian metrics and K-stability"
    with Craig Van Coevering, Int. Math. Res. Not. IMRN 2015, no. 22, 11566-11604. Journal.
    ArXiv 1312.3686


22. "Lower bounds on the modified K-energy and complex deformations"
    with Andrew Clarke, Adv. Math. 252 (2014), 449–470. Journal.
    ArXiv 1302.0556


23. "Deformations of complex structures and the coupled Kähler-Yang-Mills equations"
    with Mario Garcia-Fernandez, J. London Math. Soc. 89 (2014) 779-796. Journal.
    ArXiv 1301.4480


24. "Deformations of extremal toric manifolds"
    with Yann Rollin, J. Geom. Anal. 24 (2014), no. 4, 1929-1958. Journal.
    ArXiv 1201.4137


25. "A note on blow-ups of toric surfaces and CSC Kähler metrics"
    Tohoku Math. J. (2) Vol. 66, No. 1 (2014), 15-29. Journal.
    ArXiv 1203.0854


26. "Deformation of extremal metrics, complex manifolds and the relative Futaki invariant"
    with Yann Rollin and Santiago Simanca, Math. Z. 273 (2013), no. 1-2, 547-568. Journal.
    ArXiv 1107.0456


27. "Extremal Kähler metrics on blow-ups of parabolic ruled surfaces":
    Bulletin de la SMF 141, fascicule 3 (2013), 481-516. Journal.
    ArXiv 1104.4315

Thesis

• "Métriques extrémales et système de Strominger", Habilitation. pdf (in french)

• "Constructions de Métriques extrémales, résolutions de singularités et déformations complexes", Thesis supervised by Yann Rollin at laboratoire de mathématiques Jean Leray de Nantes. pdf (in french)

Phd Students

• Remi Delloque (2023-....) : "Perturbative techniques for geometric PDEs with moment map pictures".

• Achim Napame (2020-2023) : "Equivariant stable sheaves on toric varieties".