Research in complex geometry at IMAG, in the GTA team, I am PI of ANR-21-CE40-0011 JCJC project MARGE 2021-2025. I defended my HDR in May 2024. I belong to the French research groups RT GAS and Algèbre and I am a member of SMF, the French Mathematical Society, and European Mathematical Society.

Teaching at the mathematics department of Faculté des Sciences de Montpellier.

I have been a postdoctoral researcher at University of Strasbourg (2018-2019) and ENS-PSL (2016-2018). Before that, I was PhD student (2012-2015) then ATER (2015-2016) at UGA. I defended my PhD thesis Kähler-Einstein metrics on group compactifications in October 2015. Philippe Eyssidieux was my advisor. Going back in time, Mathematics Genealogy Project indicates that my mathematical ancestors were: Ngaiming Mok, Yum-Tong Siu, Robert Clifford Gunning, Salomon Bochner, Erhard Schmidt, David Hilbert (and I'll stop here: Hilbert has over 36000 descendants in the database!).

News

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On June 2-6 2025, I will participate in the conference Real algebraic geometry and Birational geometry at the CIRM in Marseille.

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On May 19-23 2025, I will participate in the conference Complex Hermitian Geometry in Angers.

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I will spend April 2025 in Daejeon, South Korea.

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On March 3-7 2025, I gave a mini-course at the winter school on K-stability at the CIRM in Marseille.

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On January 27-31 2025, I gave a talk at the workshop Geometric Flows and Quantization of Kähler Metrics in Brussels.

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On October 22 2024, my student Tran Trung Nghiem defended his PhD thesis in Montpellier.

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In November 2024 I co-organized the annual meeting of RT GAS, together with Benoît Cadorel and Enrica Floris. Here is the website

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Until July 2024, I was in charge of the weekly AGATA seminar in Montpellier, with Damien Calaque (see here for the official seminar website).
On June 25-28 2024, I participated in the conference Varieties with Boundaries in Wakkanai, Japan
On May 30 2024 I defended my HDR "Métriques de Kähler canoniques sur les variétés sphériques", I am now officially allowed to supervize PhD students and to apply to Professor positions in France.
On May 21-24 2024, Nivedita Viswanathan and Tiago Duarte Guerreiro visited me in Montpellier.
On May 15-17 2024, Simon Jubert visited me in Montpellier.
On April 16-19 2024, I participated in the Workshop on homogeneous varieties in Daejeon, Korea, where I gave a two hours talk.
On April 9 2024, I visited Ronan Terpereau in Lille and gave a talk at the algebraic geometry seminar.
On April 2-4 2024, Anne-Sophie Kaloghiros visited me in Montpellier.
In March 2024 I co-organized an Oberwolfach workshop on Birational geometry, Mirror symmetry and K-stability, together with Susanna Zimmermann and Liana Heuberger. The report is here.
On February 12-13 2024 I organized a MARGE workshop on real Monge-Ampère equations and SYZ conjecture in Montpellier. Jakob Hultgren visited for the week.
On January 29-30 2024, I visited Eleonora Di Nezza in Paris and gave a talk at the SAG seminar.
On March 28-29 2024, King and I visited Carl Tipler in Brest, and I gave a talk at the geometry seminar.
Together with Clément Dupont, we organized a reading seminar on logarithmic geometry in Montpellier

Earlier

2023 2022 2021 2020

Publications

Numerical invariants for weighted cscK metrics
Thibaut Delcroix and Simon Jubert
submitted
arXiv:2503.01680

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Weight sensitivity in K-stability of Fano varieties
Thibaut Delcroix
submitted
arXiv:2411.07864

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CscK metrics on rank one spherical Fano fourfolds
Thibaut Delcroix
4 pages note intended for a Proceedings volume
arXiv:2408.12893

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SYZ and optimal transport stability of Weyl polytopes
Thibaut Delcroix and Jakob Hultgren
accepted at Pure and Applied Mathematics Quarterly
arXiv:2406.02068

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Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces
Thibaut Delcroix
accepted at Bulletin of the London Mathematical Society
doi:10.1112/blms.13069   arXiv:2310.04062

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Spherical actions on locally factorial Fano varieties of dimension \(\leq 4\) and rank \(\leq 2\)
Thibaut Delcroix and Pierre-Louis Montagard
submitted
arXiv:2308.15858

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An effective weighted K-stability condition for polytopes and semisimple principal toric fibrations
Thibaut Delcroix and Simon Jubert
Annales Henri Lebesgue Volume 6 (2023), pp. 117-149.
doi:10.5802/ahl.161   arXiv:2202.02996

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The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
Thibaut Delcroix
In: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, Kähler–Einstein Metrics and Degenerations., Springer Proceedings in Mathematics & Statistics, vol 409.
doi:10.1007/978-3-031-17859-7_10   arXiv:2011.07135

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Uniform K-stability of polarized spherical varieties
Thibaut Delcroix, with an appendix by Yuji Odaka
EPIGA, Vol 7, 2023
doi:10.46298/epiga.2022.9959   arXiv:2009.06463

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Examples of K-unstable Fano manifolds
Thibaut Delcroix
Annales de l'Institut Fourier Tome 72 no. 5, 2079--2108 (2022)
Zbl 07589437   doi:10.5802/aif.3505   arXiv:1911.08300

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Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
Thibaut Delcroix and Jakob Hultgren
Journal de Mathématiques pures et appliquées (9) 153, 281--315 (2021)
Zbl 07395705   doi:10.1016/j.matpur.2020.12.002   arXiv:1812.07218

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Ricci flat Kähler metrics on rank two complex symmetric spaces
Thibaut Delcroix and Olivier Biquard
Journal de l'École Polytechnique - Mathématiques 6, 163--201 (2019)
Zbl 1431.53076   doi:10.5802/jep.91   arXiv:1807.07129

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Kähler geometry of horosymmetric varieties, and application to Mabuchi's K-energy functional
Thibaut Delcroix
Journal für die reine und angewandte Mathematik 763, 129--199 (2020)
Zbl 1446.32015   doi:10.1515/crelle-2018-0040   arXiv:1712.00221

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K-Stability of Fano spherical varieties
Thibaut Delcroix
Annales Scientifiques de l'École Normale Supérieure (4) 53, No. 3, 615--662 (2020)
Zbl 07226614   doi:10.24033/asens.2430   arXiv:1608.01852

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Kähler-Einstein metrics on group compactifications
Thibaut Delcroix
Geometric and Functional Analysis 27, No. 1, 78--129 (2017)
Zbl 1364.32017   doi:10.1007/s00039-017-0394-y   arXiv:1510.07384

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Log canonical thresholds on group compactifications
Thibaut Delcroix
Algebraic Geometry 4, No. 2, 203--220 (2017)
Zbl 1393.14050   doi:10.14231/AG-2017-010   arXiv:1510.05079

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Alpha-invariant of toric line bundles
Thibaut Delcroix
Annales Polonici Mathematici 114, No. 1, 13--27 (2015)
Zbl 1331.32010   doi:10.4064/ap114-1-2   arXiv:1409.0961

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Les groupes de Burger-Mozes ne sont pas Kählériens
Thibaut Delcroix
Annales de la Faculté des Sciences de Toulouse (6) 23, No. 1, 115--127 (2014)
Zbl 1290.32017   doi:10.5802/afst.1399   arXiv:1211.4234

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Students & Postdocs

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King Leung Lee is my postdoc in Montpellier from November 2023 to October 2025. He has already written two preprints during his stay in Montpellier: Chow stability of \(\lambda\)-stable toric varieties and On the blow-up formula of the Chow weights for polarized toric manifolds.

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After a Master 2 thesis under my direction, Bilal Maoui started in 2023 a PhD thesis under the supervision of Eleonora Di Nezza and myself.

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Tran Trung Nghiem defended in 2024 his PhD, co-supervised with Marc Herzlich, he has written four articles as part of his PhD thesis: On the regularity of conical Calabi-Yau potentials (to appear at Annales Polonici Mathematici), Spherical cones: classification and a volume minimization principle (published at Journal of Geometric Analysis), Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity and K-stable valuations and Calabi-Yau metrics on affine spherical varieties. He is now a postdoc in Lyon.

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Andréa Favier and Raphaël Planque Master 1 thesis (2022):
"Points entiers dans les polytopes convexes"
version finale

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Agathe Rolland Master 1 thesis (2021):
"Description du groupe de Lie G_2 et de son action sur S^6"
version finale

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Enseignement