My research interest is in differential geometry and partial differential equations. More precisely, I have been mainly focused on the study of Geometric Flows on non compact manifolds and especially on the geometry at infinity of self-similar solutions (solitons) of the (Kahler-)Ricci Flow, Mean Curvature Flow and the Harmonic Map Heat Flow.

• PhD work: Géométrie à l’infini de certaines variétés non compactes. 
• Steady gradient Ricci soliton with curvature in L1 Comm. Anal. Geom. 20 (2012), no. 1, 31-53.​
• Structure at infinity of expanding gradient Ricci soliton (with Chih-Wei Chen) Asian Journal of mathematics (2015), Vol. 19, no. 5.
• Rapport asymptotique de courbure, courbure positive et non effondrement  Actes de Séminaire de Théorie Spectrale et Géométrie 2011_2012.
• Stability of non compact steady and expanding gradient Ricci solitons Calculus of Variations and PDE’s, Vol. 54, (2015), p.2367-2405.
• Asymptotic estimates and compactness of expanding gradient Ricci solitons Annali Della Scuola Normale Superiore Di Pisa, Vol. 17, (2017), p.485-530.
• Smoothing out positively curved metric cones by Ricci expanders Geometric and Functional Analysis, Vol. 26, (2016), p.188-249.
• Unique continuation at infinity for conical Ricci expanders Int. Math. Res. Not. IMRN, (2017), p.3107-3147.
• Weak stability of Ricci expanders with positive curvature operator  (with Tobias Lamm) Matematische Zeitschrift, Vol. 286, (2017), p.951-985. 
• Expanding Kähler-Ricci solitons coming out of Kähler cones   (with Ronan Conlon)  Journal of Differential Geometry. Vol. 115, (2020), p.303-365.
• Stability of ALE Ricci-flat manifolds under Ricci flow (with Klaus Kröncke)The Journal of geometric analysis, Vol. 30, (2020), p.2829-2870.
• Existence of expanders of the harmonic map flow(with Tobias Lamm) Annales de l’École Normale Supérieure, Vol.54, (2021), p.1237-1274.
• A relative entropy for expanders of the harmonic map flow   Communications in Partial Differential Equations, Vol. 44, (2019), p.1481-1541.
• Generic uniqueness of expanders with vanishing relative entropy (with Felix Schulze) Mathematische Annalen, Vol. 377, (2020), p.1095-1127.
• On the regularity of Ricci flows coming out of metric spaces (with Felix Schulze and Miles Simon)  Journal of European Mathematical Society, Vol. 24, (2022), p.2233-2277. 
• Classification results for expanding and shrinking gradient Kahler-Ricci solitons (with Ronan Conlon and Song Sun)   Accepté pour publication à Geometry and Topology. arXiv:1904.00147
• Steady gradient Kahler-Ricci solitons on crepant resolutions of Calabi-Yau cones (with Ronan Conlon)  Accepté pour publication à Memoirs of the American Mathematical Society. arXiv:2006.03100 
• A Lojasiewicz inequality for ALE Ricci-flat metrics (with Tristan Ozuch) Submitted. arXiv:2007.09937 
• A relative entropy and a unique continuation result for Ricci expanders (with Felix Schulze)  Accepté pour publication à Communication on Pure and Applied Mathematics. arXiv:2101.02638
• Dynamical (in)stability of Ricci-flat ALE metrics along the Ricci flow (with Tristan Ozuch)  Accepté pour publication à Calculus of Variations and PDE’s. arXiv:2104.10630  
• Uniform estimates for cscK metrics (with Eleonora DiNezza). Annales de la Faculté des Sciences de Toulouse. Mathématiques. Vol. 31, (2022), p.975-993.
• On finite Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces (with Charles Cifarelli and Ronan Conlon). Submitted. arXiv:2203.04380
• Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds (with Felix Schulze and Miles Simon), Submitted. arXiv:2203.15313
• A new complete two-dimensional shrinking gradient Kähler-Ricci soliton (with R. Bamler, C. Cifarelli and R. Conlon). Submitted. arXiv:2206.10785
• An Aubin continuity path for shrinking gradient Kähler-Ricci solitons (with C. Cifarelli, R. Conlon, A. Deruelle). Submitted. arXiv:2205.08482