I mainly work in holomorphic dynamics, at the intersection between dynamics systems (especially ergodic theory) and complex analysis (complex geometry and pluripotential theory).
Some more precise (and often overlapping) areas I have worked on are as follows.
A. Dynamics of (usually higher dimensional) holomorphic dynamical systems [12,16,17,19,20,21,28]
B. Global stability and bifurcations in (usually higher dimensional) holomorphic dynamics [2,3,4,6,7,8,10,14,22]
C. Thermodynamic formalism and applications in holomorphic dynamics [11,15,23,24,25,26,29]
D. Local parabolic dynamics (parabolic implosion, meromorphic connections on Riemann surfaces) [1,5,18,27]
E. Levi currents and complex manifolds [9,13]
My Arxiv author page is here. Preprints usually appear there before than on this page.
Most of the recent papers are also on HAL.
The arXiv and Hal versions are usually not final. Please refer to the journal webpages (or email me) for the final versions of the papers below.
29. A thermodynamic path metric for complex Hénon maps (with Yan Mary He), 2026,
pdf,
arXiv,
28. On the support of measures of large entropy for automorphisms of Kaehler manifolds (with Sobir Boymurodov and Karim Rakhimov), 2026
pdf,
arXiv,
27. Non-autonomous parabolic implosion (with Matthieu Astorg), 2026
pdf,
arXiv,
26. A Ruelle-McMullen formula for the volume dimension of skew products in C^2 (with Yan Mary He), 2026,
pdf,
arXiv,
25. Analyticity of the Hausdorff dimension and metric structures on Misiurewicz families of polynomials (with Yan Mary He), 2025,
pdf,
arXiv,
HAL,
24. Manhattan curves in complex dynamics and asymptotic correlation of multiplier spectra (with Yan Mary He), 2025,
pdf,
arXiv,
HAL,
Contemporary Mathematics, to appear
23. Pressure path metric on parabolic families of polynomials (with Yan Mary He), 2024,
pdf,
arXiv,
HAL
Indiana University Mathematics Journal, to appear
22. Holomorphic motions of weighted periodic points (with Maxence Brévard)
pdf,
arXiv,
HAL
Algebraic, Complex, and Arithmetic Dynamics (Simons Symposia Series), 2026
21. Hölder continuity and laminarity of the Green currents for Hénon-like maps(with Tien-Cuong Dinh and Karim Rakhimov),
pdf,
arXiv,
HAL
Journal of the Institute of Mathematics of Jussieu,
Volume 25, Issue 2, March 2026, 1363-1392
20. Exponential mixing of all orders and CLT for automorphisms of compact Kaehler manifolds (with Tien-Cuong Dinh),
pdf,
arXiv,
HAL,
Advances in Mathematics, Volume 485, February 2026, 110689
19. On the support of measures of large entropy for polynomial-like maps (with Sardor Bazarbaev and Karim Rakhimov),
pdf,
arXiv,
HAL,
Analysis and Mathematical Physics,
Volume 15, article number 69, 2025
18. Horn maps of semi-parabolic Hénon maps (with Matthieu Astorg),
pdf,
arXiv
HAL,
Mathematische Annalen
Volume 392, pages 837-860, 2025
17. A Mané-Manning formula for expanding measures for endomorphisms of CPk(with Yan Mary He),
pdf,
arXiv,
HAL
Transactions of the AMS,
Volume 377, Number 11, 8179-8219, 2024
16. Monotonicity of dynamical degrees for horizontal-like and polynomial-like maps (with Tien-Cuong Dinh and Karim Rakhimov),
pdf,
arXiv,
HAL
Transactions of the AMS,
Volume 377, Number 9, 6595-6618, 2024
15. Equilibrium states of holomorphic endomorphisms of CP(k): spectral stability and limit theorems (with Tien-Cuong Dinh),
pdf,
arXiv,
HAL
Geometric and Functional Analysis (GAFA), Volume 34, 1006–1051, 2024
(for the original version containing both this and the part I below:
pdf,
arXiv,
HAL)
An (online) seminar about this work: Video
A 4x1h30 mini-course about the work:
Lecture 1,
Lecture 2,
Lecture 3,
Lecture 4
14. Strong probabilistic stability in holomorphic families of endomorphisms of Pk and polynomial-like maps (with Karim Rakhimov),
pdf,
arXiv,
HAL
International Mathematics Research Notices (IMRN),
Volume 2024, Issue 12, 9875–9892, 2024
13. Generalized Levi currents and Singular loci for families of plurisubharmonic functions (with Samuele Mongodi),
pdf,
arXiv,
HAL
Journal of Geometric Analysis, Volume 34, article number 203, 2024
12. Every Hénon map is exponentially mixing of all orders and satisfies the CLT (with Tien-Cuong Dinh), 2023,
pdf,
arXiv,
HAL
Forum of Mathematics, Sigma, Volume 12, article e4, 2024
A seminar about this work: Video
11. Equilibrium states of holomorphic endomorphisms of CP(k) I: existence and properties (with Tien-Cuong Dinh),
pdf,
arXiv,
HAL
Journal de Mathématiques Pures et Appliquées, Volume 172, 164-201, 2023
(see above for the part II and videos of a seminar and of a mini-course on this work)
10. Hyperbolicity and bifurcations in holomorphic families of polynomial skew products (with Matthieu Astorg),
pdf,
arXiv,
HAL
American Journal of Mathematics, Volume 145, Number 3, 861-898, 2023
9.
On minimal kernels and Levi currents on weakly complete complex manifolds (with Samuele Mongodi)
pdf,
arXiv,
HAL
Proceedings of the AMS, Volume 150, Issue 9, 3927–3939, 2022
8. Higher bifurcations for polynomial skew products (with Matthieu Astorg)
pdf,
arXiv,
HAL
Journal of Modern Dynamics, 18, 69-99, 2022
A recorded seminar about this work: Video
7. Degeneration of quadratic polynomial endomorphisms to a Hénon map (with Yusuke Okuyama),
pdf,
arXiv
Indiana University Mathematics Journal, Volume 69, 2549-2570, 2020
6. Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree,
pdf,
arXiv,
HAL
Mathematische Annalen, Volume 373, 901–928, 2019
5. Parabolic implosion for endomorphisms of C^2,
pdf,
arXiv,
HAL
Journal of the European Mathematical Society (JEMS), Volume 21, 3709-3737, 2019
4. Perturbations d'exemples de Lattès et dimension de Hausdorff du lieu de bifurcation (with François Berteloot),
pdf,
arXiv,
HAL
Journal de Mathématiques Pures et Appliquées, Volume 116, 161–173, 2018
3. Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
(with François Berteloot and Christophe Dupont),
pdf, arXiv,
HAL
Annales Scientifiques de l’ENS, Volume 51, Issue 1, 215-262, 2018
2. Bifurcations in the elementary Desboves family (with Johan Taflin),
pdf,
arXiv,
HAL
Proceedings of the AMS, Volume 145, Issue 10, 4337-4343, 2017
1. A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces
(with Marco Abate),
pdf, arXiv
Mathematische Zeitschrift,
Volume 282, Issue 1, 247–272, 2016
IMS/NUS report for the Conference Recent Developments in Algebraic Geometry, Arithmetic and Dynamics Part 2, 2023
Oberwolfach report for the workshop Complex Geometry and Dynamical Systems, 2022
Equidistribution en dynamique holomorphe (with Lucas Kaufmann), 2026,
pdf,
Gazette de la SMF, to appear
Statistical properties of complex Hénon maps (with Tien-Cuong Dinh), in Hénon maps: a list of open problems (Eds. C. Favre, T. Firsova, L. Palmisano, J. Raissy, G. Vigny), 2023,
arXiv
Arnold Mathematical Journal, 2024
Stability and bifurcations in projective holomorphic dynamics (with François Berteloot),
pdf
Dynamical systems, Banach Center Publications, 115, Polish Acad. Sci. Inst. Math., Warsaw, 37–71, 2018.
Editor for Quantitative aspects in complex analysis, geometry, and dynamics,
Springer, CEMPI Lecture Notes Series
Volume of collected lecture notes of the School and Workshop ACQUA21
In preparation
Reporter for the
Oberwolfach report for the workshop Complex Geometry and Dynamical Systems, 2022
Thermodynamics and Bifurcations in Several Complex Variables,
HDR manuscript,
pdf
Motions of Julia sets and dynamical stability in several complex variables,
PhD Thesis,
pdf
Geodesics for meromorphic connections
on Riemann surfaces and dynamics of homogeneous vector
fields in several complex variables,
Master Thesis,
pdf