Thibaut Delcroix
photo de face de T. Delcroix

Maître de Conférences at University of Montpellier since 2019

Email: thibaut.delcroixumontpellier.fr

Address: IMAG, c.c. 051
Université de Montpellier
Place Eugène Bataillon
34095 Montpellier Cedex 5
(office 308, building 9, campus map)

ORCIDzbMatharXivHALResearchGate

Research in complex geometry at IMAG, in the GTA team, I am PI of ANR-21-CE40-0011 JCJC project MARGE 2021-2025. I belong to the French research groups GDR GAGC and TLAG 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 currently teach a third year course 'Calcul différentiel et équations différentielles' and a Problem Based Learning course for first year Biology students.

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 2023


Together with Clément Dupont, we organize a reading seminar on logarithmic geometry in Montpellier


On June 25-28 2024, I will participate in the conference Varieties with Boundaries in Wakkanai, Japan


On April 16-19 2024, I will participate in the Workshop on homogeneous varieties in Daejeon, Korea


In 2024 I will be co-organizing an Oberwolfach workshop on Birational geometry, Mirror symmetry and K-stability, together with Susanna Zimmermann and Liana Heuberger


On February 12-15 2024 I will run an informal MARGE workshop on real Monge-Ampère equations and SYZ conjecture in Montpellier


In 2024 I will be co-organizing the biannual meeting of GDR GAGC, together with Benoît Cadorel and Enrica Floris


I am in charge of the weekly AGATA seminar in Montpellier, with Damien Calaque (see here for the official seminar website).


On April 9 2024, I will be visiting Ronan Terpereau in Lille
On January 29-30 2024, I will be visiting Eleonora Di Nezza in Paris
On March 28-29 2024, I will be visiting Carl Tipler in Brest
On November 23 2023, I gave a talk at the Online Algebraic Geometry Seminar
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 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 March 23-24, 2023, I organized the (final?) FIBALGA workshop in Montpellier.
On April 10-14 2023, I attended the Oberwolfach workshop "Komplexe Analysis - Differential and Algebraic methods in Kähler spaces".

Earlier


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

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.161arXiv: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_10arXiv: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.2022.9959arXiv:2009.06463

Examples of K-unstable Fano manifolds
Thibaut Delcroix
Annales de l'Institut Fourier Tome 72 no. 5, 2079--2108 (2022)
Zbl 07589437doi:10.5802/aif.3505arXiv: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 07395705doi:10.1016/j.matpur.2020.12.002arXiv: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 1431.53076doi:10.5802/jep.91arXiv: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 1446.32015doi:10.1515/crelle-2018-0040arXiv: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 07226614doi:10.24033/asens.2430arXiv:1608.01852
Kähler-Einstein metrics on group compactifications
Thibaut Delcroix
Geometric and Functional Analysis 27, No. 1, 78--129 (2017)
Zbl 1364.32017doi:10.1007/s00039-017-0394-yarXiv:1510.07384
Log canonical thresholds on group compactifications
Thibaut Delcroix
Algebraic Geometry 4, No. 2, 203--220 (2017)
Zbl 1393.14050doi:10.14231/AG-2017-010arXiv:1510.05079
Alpha-invariant of toric line bundles
Thibaut Delcroix
Annales Polonici Mathematici 114, No. 1, 13--27 (2015)
Zbl 1331.32010doi:10.4064/ap114-1-2arXiv: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 1290.32017doi:10.5802/afst.1399arXiv:1211.4234

Students & Postdocs


King Leung Lee is my postdoc from November 2023.
After a Master 2 thesis under my direction, Bilal Maoui is starting 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 three 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), and Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity.
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, 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

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

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

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

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