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
On June 2-6 2025, I will participate in the conference Real algebraic geometry and Birational geometry at the CIRM in Marseille.
On May 19-23 2025, I will participate in the conference Complex Hermitian Geometry in Angers.
I should spend April 2025 in Daejeon, South Korea.
On March 3-7 2025, I will give a mini-course at the winter school on K-stability at the CIRM in Marseille.
On January 27-31 2025, I will participate in the workshop Geometric Flows and Quantization of Kähler Metrics in Brussels.
On October 22 2024, my student Tran Trung Nghiem will defend his PhD thesis in Montpellier.
In November 2024 I co-organize the annual meeting of RT GAS, together with Benoît Cadorel and Enrica Floris. Here is the website
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
On March 23-24, 2023, I organized the (final?) FIBALGA workshop in Montpellier.
On May 15-19 2023, I participated in the International conference "Workshop on Moduli, K-stability, Fano varieties, and related topics" at IBS in Daejeon, Republic of Korea. I gave two 1-hour talks (slides for talk1 and talk2) on effective K-stability of spherical varieties, the first talk giving an introduction to spherical varieties via a WIP on the classification of spherical Fano fourfolds with Pierre-Louis Montagard.
On September 25-29 2023, I participated in the CMI Workshop K-stability and Birational Geometry in Oxford, UK, and I gave a talk on my preprint with Pierre-Louis Montagard.
On November 23 2023, I gave a talk at the Online Algebraic Geometry Seminar
On April 10-14 2023, I attended the Oberwolfach workshop "Komplexe Analysis - Differential and Algebraic methods in Kähler spaces".
June 2-3 2022: I organized the first workshop of ANR MARGE: Young researchers in Kähler and Hermitian geometry, Montpellier
First half of 2022: I organized the online reading seminar Weighted cscK metrics and semisimple principal fibrations
On January 5-7 2022, I gave a series of three two-hours lectures on canonical Kähler metrics on spherical varieties, online at the Ensemble of Algebra and Geometry seminar, here are the lecture notes, with some minor typos Lecture 1, Lecture 2 and Lecture 3.
On December 11-14 2022, I visited Sébastien Boucksom in Paris.
On November 23 2022, I gave a talk at Edge days 2022 (21-25 November) in Edinburgh.
October 30 to November 4 2022, I visited Eleonora Di Nezza in Paris.
On October 24-25 2022, Pierre-Alexandre Gillard visited me in Montpellier. On July 10-13 I visited Olivier Biquard, Sébastien Boucksom and Eleonora Di Nezza in Paris.
June 27 to July 1, Tiago Duarte Guerreiro visited me in Montpellier.
On June 21-23 2022, I gave a talk at the International Workshop Kähler and non-Kähler Geometry: New Developments and Interactions in Aarhus.
On June 15 2022, I gave a talk at the virtual seminar on Geometry with Symmetries.
May 29 to June 3 2022: Annamaria Ortu and Carlo Scarpa visited me in Montpellier.
April-May 2022, I organized a local reading seminar on plurisubharmonic functions and the Monge-Ampère operator.
On May 19-20 2022, I gave a talk at the Journées d'études TLAG 2022.
On May 9 2022, I gave a talk at the séminaire de géométrie complexe in Nancy.
On April 28 2022, I gave a talk at the special session "Group actions on varieties" of Korean Mathematical Society Spring Meeting 2022 (slides).
On March 25 2022, I gave a talk at the séminaire de géométrie in Nantes.
On March 9-11 2022, I gave a talk at the FIBALGA workshop Poitiers 2022.
On March 3-4 2022, I visited Eveline Legendre and Simon Jubert in Toulouse.
Together with Pierre-Louis Montagard, we organized the Journées d'étude du GDR TLAG 2021 on June 24-25 2021.
Together with Georgios Kydonakis and Florent Schaffhauser, we organized the conference Geometric and Analytic aspects of moduli spaces of Higgs bundles online, on June 7-11 2021.
On July 5-9 2021, I visited Chinh Lu, Sébastien Boucksom, Olivier Biquard and Paul Gauduchon in Paris.
On June 14-18 2021, I gave a talk at the Algebraic Geometry in Angers conference.
May 31 to June 4 2021, I attended AMAZER conference to celebrate Ahmed Zeriahi.
On May 25 2021, I gave an online talk at the School of mathematics and statistics, Beijing Insitute of Technology, invited by Yan Li.
On April 29 2021, I gave a talk at the Séminaire de géométrie complexe in Toulouse.
On March 18-19 2021, I gave a talk at the FIBALGA 2021 Workshop in Dijon.
On January 22 2021, I gave an online talk at Tokyo Tech geometry seminar, invited by Yoshinori Hashimoto.
On January 11 2021, I gave an online talk at the Séminaire ANH of Insitut de Mathématiques d'Orsay, invited by Chinh Lu.
On January 5 2021, I gave an online talk at the Geometry seminar of Lisbonne, invited by Rosa Sena Dias.
Together with Clément Dupont, we ran a reading seminar on Théorie de Hodge en combinatoire in 2020 (in French).
On August 17-21 I gave an online talk at Oberwolfach workshop "Komplexe Analysis: algebraicity and transcendence".
Publications
CscK metrics on rank one spherical Fano fourfoldsThibaut Delcroix
4 pages note intended for a Proceedings volume
arXiv:2408.12893
SYZ and optimal transport stability of Weyl polytopes
Thibaut Delcroix and Jakob Hultgren
accepted at Pure and Applied Mathematics Quarterly
arXiv:2406.02068
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
Spherical actions on locally factorial Fano varieties of dimension \(\leq 4\) and rank \(\leq 2\)
Thibaut Delcroix and Pierre-Louis Montagard
preprint
arXiv:2308.15858
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
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
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
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
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
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
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
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
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
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
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
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
Students & Postdocs
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.
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.
Tran Trung Nghiem is currently my PhD student, 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.
Andréa Favier and Raphaël Planque Master 1 thesis (2022):
"Points entiers dans les polytopes convexes"
version finale
Agathe Rolland Master 1 thesis (2021):
"Description du groupe de Lie G_2 et de son action sur S^6"
version finale
Enseignement
HAX502X - Calcul différentiel et équations différentielles, 2023-2024
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cours, DM
HAV114X - Mathématiques calculatoires en APP, 2022-2023
Co-responsable UE avec Thomas Hausberger, cours, TD
L1 Biologie, parcours Apprentissage Par Problèmes, mais plus pour l'UE de Math cette année contrôle final
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cours, DM
HAV114X - Mathématiques calculatoires en APP, 2022-2023
Co-responsable UE avec Thomas Hausberger, cours, TD
L1 Biologie, parcours Apprentissage Par Problèmes, mais plus pour l'UE de Math cette année contrôle final
HAX502X - Calcul différentiel et équations différentielles, 2022-2023
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cf HLMA602 années précédentes pour l'essentiel du cours et des TD
HAV114X - Mathématiques calculatoires en APP, 2022-2023
Co-responsable UE avec Thomas Hausberger, cours, TD et tutorat
L1 Biologie, parcours Apprentissage Par Problèmes
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cf HLMA602 années précédentes pour l'essentiel du cours et des TD
HAV114X - Mathématiques calculatoires en APP, 2022-2023
Co-responsable UE avec Thomas Hausberger, cours, TD et tutorat
L1 Biologie, parcours Apprentissage Par Problèmes
Encadrement du TER d'Andréa Favier et Raphaël Planque 2022 :
"Points entiers dans les polytopes convexes"
HAS202X - Outils Mathématiques 3, 2021-2022
un groupe de TD
L1 Chimie
HAX604X - Analyse numérique des équations différentielles, 2021-2022
un groupe de TD
L3 Math
HAX707X - Groupes et géométrie, 2021-2022
Responsable UE, cours et TD
M1 Math
Documents : contrôle final, cf HMMA114 années précédentes pour l'essentiel du cours et des TD
HAX502X - Calcul différentiel et équations différentielles, 2021-2022
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cf HLMA602 années précédentes pour l'essentiel du cours et des TD
HAV114X - Mathématiques calculatoires en APP, 2021-2022
Co-responsable UE avec Thomas Hausberger, cours, TD et tutorat
L1 Biologie, parcours Apprentissage Par Problèmes
"Points entiers dans les polytopes convexes"
HAS202X - Outils Mathématiques 3, 2021-2022
un groupe de TD
L1 Chimie
HAX604X - Analyse numérique des équations différentielles, 2021-2022
un groupe de TD
L3 Math
HAX707X - Groupes et géométrie, 2021-2022
Responsable UE, cours et TD
M1 Math
Documents : contrôle final, cf HMMA114 années précédentes pour l'essentiel du cours et des TD
HAX502X - Calcul différentiel et équations différentielles, 2021-2022
Responsable UE, cours et TD
L3 Math
Documents : contrôle final, cf HLMA602 années précédentes pour l'essentiel du cours et des TD
HAV114X - Mathématiques calculatoires en APP, 2021-2022
Co-responsable UE avec Thomas Hausberger, cours, TD et tutorat
L1 Biologie, parcours Apprentissage Par Problèmes
Encadrement du TER d'Agathe Rolland 2021 :
"Description du groupe de Lie G_2 et de son action sur S^6"
version finale
HLMA602 - Calcul différentiel et équations différentielles, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HLMA412 - Compléments d'analyse, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HMMA114 - Géométrie et groupes classiques, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HLMA103 - BioMaths, 2020-2021
quelques TD
Documents : quelques feuilles de TD corrigées
"Description du groupe de Lie G_2 et de son action sur S^6"
version finale
HLMA602 - Calcul différentiel et équations différentielles, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HLMA412 - Compléments d'analyse, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HMMA114 - Géométrie et groupes classiques, 2020-2021
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
HLMA103 - BioMaths, 2020-2021
quelques TD
Documents : quelques feuilles de TD corrigées
HLMA602 - Calcul différentiel et équations différentielles, 2019-2020
TD
voir la page web de Matthieu Alfaro pour le poly cours-TD
HLMA412 - Compléments d'analyse, 2019-2020
Responsable UE, cours et TD
Documents : poly de cours-TD, sujet d'examen
HMMA114 - Géométrie et groupes classiques, 2019-2020
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen
TD
voir la page web de Matthieu Alfaro pour le poly cours-TD
HLMA412 - Compléments d'analyse, 2019-2020
Responsable UE, cours et TD
Documents : poly de cours-TD, sujet d'examen
HMMA114 - Géométrie et groupes classiques, 2019-2020
Responsable UE, cours et TD
Documents : poly de cours, feuilles de TD, sujet d'examen