Scientific interests

Overview

During my PhD, I constructed geometric boundaries at infinity for some asymptotically complex hyperbolic Kähler manifolds. This result is the analogue of that obtained by Bahuaud-Gicquaud-Lee-Marsh in the real hyperbolic setting. I then generalised this result to the almost Hermitian case.
In Stockholm, with Klaus Kröncke and Francesca Oronzio, we established a Positive Mass Theorem for asymptotically hyperbolic 3-manifolds via the theory of potentials.
I am currently investigating constructions of 1-parameter families of Poincaré-Einstein metrics degenerating towards complex hyperbolic Einstein metrics.

Keywords

• Differential and Riemannian geometry
• Negatively curved manifolds
• Einstein metrics
• Geometric analysis
• Elliptic theory

Scientific production

Prepublications

3. Green functions and a positive mass Theorem for asymptotically hyperbolic 3-manifolds
   with Klaus Kröncke and Francesca Oronzio [arXiv:2506.07108]
   Abstract

   We prove a monotonicity formula that holds along the level sets of the Green's function of an asymptotically hyperbolic 3-manifold. We then use it to prove a positive mass Theorem for the volume-renormalized mass, recently introduced by M. Dahl, K. Kröncke and S. McCormick.

Publications

2. CR compactification for asymptotically locally complex hyperbolic almost Hermitian manifolds
   The Journal of Geometric Analysis 34(8), 238 (2024) [journal · arXiv:2307.04062]
   Abstract

   This article extends the result of [1] to the case of almost Hermitian manifolds \((M,g,J)\), for which the almost complex structure \(J\) is not parallel (and in fact \(J\) is not integrable, and the almost symplectic form \(\omega = g(J\cdot,\cdot)\) is not closed). We also lower the assumption on the decay rate \(a\). We show that if \[ \|R-R^0\|_g,\quad \|\nabla R\|_g,\quad \|\nabla J\|_g,\quad \|\nabla^2 J\|_g = \mathcal{O}(e^{-ar}), \quad a>1, \] then \((M,J)\) arises as the interior of an almost complex manifold with strictly pseudoconvex, integrable, CR boundary of class \(\mathcal{C}^1\). In addition, the metric \(g\) is asymptotically complex hyperbolic, and one recovers the CR structure of the boundary by analysing the asymptotic development of the metric near infinity.
   This yields a geometric characterisation of asymptotically complex hyperbolic almost Hermitian manifolds.
3. Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds
   Mathematische Zeitschrift 307(1), 8 (2024) [journal · arXiv:2201.12132]
   Abstract

   Let \((M,g,J)\) be a complete noncompact Kähler manifold of dimension greater or equal to \(4\), \(R\) its curvature tensor, and \(R^0\) that of the complex hyperbolic space. We show that if there exists \(a>3/2\) with \[ \|R-R^0\|_g, \quad \|\nabla R \|_g = \mathcal{O}(e^{-ar}), \] then \((M,g,J)\) has a boundary at infinity, which is constructed geometrically, and which is a strictly pseudoconvex CR manifold of class \(\mathcal{C}^1\). Moreover, the Riemannian metric \(g\) is asymptotically complex hyperbolic: the CR structure at infinity is recovered by analysing the asymptotic development of \(g\) near infinity.
   This result yields a geometric characterisation of asymptotically complex hyperbolic Kähler manifolds.

PhD thesis

• Asymptotically complex hyperbolic geometry and curvature constraints
  Université de Montpellier [HAL]
  Abstract

  In this thesis, we investigate the asymptotic geometric properties of a class of complete and non compact Kähler manifolds we call asymptotically locally complex hyperbolic manifolds. The local geometry at infinity of such a manifold is modeled on that of the complex hyperbolic space, in the sense that its curvature is asymptotic to that of the model space. The natural geometric assumptions, we show that this constraint on the curvature ensures the existence of a rich geometry at infinity: we can endow it with a strictly pseudoconvex CR boundary at infinity.

Physics

• Probing Large \(N_f\) through schemes [arXiv:2507.16504]
  with Shahram Vatani
  
  Abstract

  We investigate the reliability of the large \(N_f\) expansion of four-dimensional gauge-fermion quantum field theories, focusing on the structure and scheme dependence of the beta function. While the existence of a nontrivial UV fixed point at leading order in \(1/N_f\) suggests the possibility of asymptotic safety, the absence of higher-order terms precludes robust conclusions. We analyze the impact of renormalization scheme transformations and show that higher-order corrections inevitably introduce increasingly singular contributions. We prove that at most one renormalization scheme can preserve the dominance of the leading contribution, rendering the truncation trustworthy; in all other schemes, higher-order terms dominate and the expansion becomes unreliable. This result places strong constraints on the physical interpretation of UV fixed points in large \(N_f\) theories and emphasizes the need for resummation or non-perturbative control to establish asymptotic safety.

• Novel Consistency Conditions for Fixed Point Dynamics [arXiv:2504.05988]
  with Oleg Antipin, Francesco Sannino, and Shahram Vatani
  
  Abstract

  We gain insight on the fixed point dynamics of \(d\) dimensional quantum field theories by exploiting the critical behavior of the \(d-\epsilon\) sister theories. To this end we first derive a self-consistent relation between the \(d-\epsilon\) scaling exponents and the associated \(d\) dimensional \(\beta\)-functions. We then demonstrate that to account for an interacting fixed point in the original theory the related \(d-\epsilon\) scaling exponent must be multi-valued in \(\epsilon\). We elucidate our findings by discussing several examples such as the QCD Banks-Zaks infrared fixed point, QCD at large number of flavors, as well as the \(O(N)\) model in four dimensions. For the latter, we show that although the \(1/N\) corrections prevent the reconstruction of the renormalization group flow, this is possible when adding the \(1/N^2\) contributions.

Talks

Conferences

• 01/13/2026: Journées d'Analyse Géométrique, Roscoff
• 10/14/2025: Géométrie : Échanges et Perspectives, Institut Henri Poincaré, Paris
• 08/12/2023: Einstein Spaces and Special Geometry, Mittag-Leffler Institute, Stockholm (slides)

Seminars

• 04/17/2026: Journée d'analyse, Université Catholique de Louvain
• 03/11/2026: Geometry and Topology seminar, University College London
• 02/17/2026: Séminaire d'analyse harmonique, Orsay
• 01/09/2026: Geometry and Dynamics seminar, Lille
• 12/11/2025: Spectral theory and geometry seminar, Grenoble
• 10/17/2025: Séminaire Darboux, Montpellier
• 02/06/2025: Geometry seminar, Marseille
• 12/16/2024: Geometry seminar, Nancy
• 11/29/2024: Geometry seminar, Brest
• 09/14/2024: Geometry seminar, Université Libre de Bruxelles
• 06/11/2024: Geometry seminar, Max Planck Institute, Leipzig
• 01/08/2024: Geometry seminar, Université Libre de Bruxelles
• 04/06/2023: Geometry seminar, Marseille
• 03/24/2023: Geometry seminar, Nantes
• 03/06/2023: Geometry seminar, Francfort
• 03/02/2023: Differential geometry seminar, KTH Stockholm
• 11/20/2022: Differential geometry seminar, KTH Stockholm
• 05/24/2022: Geometry seminar, Tours
• 05/13/2022: Differential geometry seminar, KTH Stockholm
• 02/16/2022: Geometry seminar, groupes et dynamique, ENS de Lyon
• 01/27/2022: Spectral theory and geometry seminar, Grenoble
• 12/17/2021: Darboux seminar, Montpellier

Workshops

• 02/10/2026: JMP Workshop Coulomb Gases, Oppedette
• 12/03/2025: Closing seminar of the ARC project "PDEs in Interactions", Spa
• 10/02/2025: Block seminar on Scalar Curvature Rigidity, Sulzbürg
• 06/11/2025: JMP Workshop Embedded Contact Homology, Chabestan
• 01/16/2025: EOS Workshop Beyond Symplectic Geometry, Antwerp
• 11/20/2024: JMP Workshop Homologie de Floer, Les Plantiers
• 05/10/2022: Block seminar on Einstein 4-manifold, Sulzbürg
• 02/08/2019: Workshop Scalar curvature and rigidity, Montpellier
• 02/06/2019: Workshop Scalar curvature and rigidity, Montpellier

PhD students seminars

• 11/18/2020: Montpellier
• 02/08/2020: ENS de Lyon & Lyon 1
• 02/09/2019: Montpellier