Research interests :
- 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
- "Foldable fans, cscK surfaces and local K-moduli",
ArXiv
2402.01159
- "Toric sheaves and flips",
with Andrew Clarke and Achim Napame. ArXiv
2309.09267
- "On the Futaki invariant of Fano threefolds",
with Lars Martin Sektnan, Ann. Univ. Ferrara 70, 811–837 (2024).
Journal.
ArXiv
2307.02258
- "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. Video
- "A note on stable toric sheaves of low rank",
Arxiv 2307.02822
- "Blowing-up Hermitian Yang--Mills connections",
with Andrew Clarke. ArXiv
2301.00525
- "Analytic K-semistability and wall-crossing",
with Lars Martin Sektnan. ArXiv
2212.08383
- "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
- "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
- "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
- "The Zariski-Lipman conjecture for toric varieties",
J. Algebra, 609 (2022), pp. 547-551.
Journal.
ArXiv
2202.02109
- "Gauge theory for string algebroids",
with Mario Garcia-Fernandez and Roberto Rubio, J. Differential Geom. 128(1): 77-152 (2024).
Journal.
ArXiv
2004.11399
- "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
- "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
- "Relative Chow stability
and optimal weights",
Proc. Amer. Math. Soc., vol. 151, no. 9 (2023), 4015-4026.
Journal.
ArXiv
1710.02536
- "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
- "Holomorphic string
algebroids",
with Mario Garcia-Fernandez and
Roberto Rubio, Trans. Amer. Math. Soc. 373 (2020), 7347-7382. Journal.
ArXiv
1807.10329
- "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
- "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
- "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
- "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
- "Lower bounds on the
modified K-energy and complex deformations"
with Andrew Clarke, Adv. Math. 252 (2014),
449–470. Journal.
ArXiv
1302.0556
- "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
- "Deformations of
extremal toric manifolds"
with Yann Rollin, J.
Geom. Anal. 24 (2014), no. 4, 1929-1958. Journal.
ArXiv
1201.4137
- "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
- "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
- "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".
|
|