Academic employment

• Assistant Professor in Mathematics, National Taiwan University, Taipei, 2022

• Research Associate, New York University - Abu Dhabi campus, 2015-2022

Education

• Ph.D in Mathematics, Université Sorbonne Paris Nord, 2014

• M.S in Mathematics, Université Sorbonne Paris Nord & Université d'Orléans, 2011

• B.S in Mathematics and Computer Science, University of Science, Ho Chi Minh City, 2010

My CV

Research Interests: Partial Differential Equations

My research deals with the mathematical study of Nonlinear Partial Differential Equations (PDEs) arising from physics, chemistry, geometry, and biology. I have a particular interest in the study of singularity formation in Nonlinear PDEs. A singularity is formally understood as starting from a very smooth initial situation and after a time, an infinity shows up in the solution or in one of its derivatives. A fascinating aspect of studying singularities is that it describes a great variety of phenomena appearing in natural sciences and beyond. Some examples of singularities that are often crucial for their appearance in experiments or numerical simulations include reaction-diffusion equations, geometric evolution equations, nonlinear dispersive equations, free-surface flows, Euler dynamics, Bose-Einstein condensates, nonlinear wave physics, bacterial growth, black-hole cosmology, etc. Singularities often correspond to the limiting behavior of mathematical models and hence are of paramount importance in understanding their behavior. My research objective is to develop mathematical tools to analyze the formation of singularity which is one of the modern research topics relevant for the field.  Some mathematical models I have been working on

    - semilinear parabolic equations/systems;

    - geometric evolution equations: the harmonic map heat flow, and wave maps;

    - nonlinear Aggregation-Diffusion equations: the Keller-Segel system;

    - semilinear wave equations.

I also enjoy programming and doing numerical simulations of PDEs.

Selected publications (completed list: MathSciNet)

• Infinitely many self-similar blow-up profiles for the Keller-Segel system in dimensions 3 to 9, arXiv, 2025 (with Z. Wang, K. Zhang)

• Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system, arXiv, 2025 (with Thomas Y. Hou, P. Song)

• Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system, arXiv, 2024 (with C. Collot, T. Ghoul, N. Masmoudi)

• On the stability of blowup solutions to the complex Ginzburg-Landau equation in R^d, arXiv, 2024 (with J. Chen, Thomas Y. Hou, Y. Wang)

• L2-based stability of blowup with log correction for semilinear heat equation, arXiv, 2024 (with Thomas Y. Hou, Y. Wang)

• Construction of type I-Log blowup for the Keller-Segel system in dimensions 3 and 4,  Annals of PDE, arXiv, 2023 (with N. Nouaili, H. Zaag)

• Collapsing-ring blowup solutions for the Keller-Segel system in three dimensions and higher, Journal of Functional Analysis, 2023 (with C. Collot, T. Ghoul, N. Masmoudi)

• Spectral analysis for singularity formation of the two-dimensional Keller-Segel system, Annals of PDE, 2022. (with C. Collot, T. Ghoul, N. Masmoudi)

• Refined description and Stability of singular solutions for the two-dimensional Keller-Segel system, Comm. Pure Appl. Math., 2021. (with C. Collot, T. Ghoul, N. Masmoudi)

• Construction of type I blowup solutions for a higher order semilinear parabolic equation, Adv. Nonlinear Anal. 2020. (with T. Ghoul, H. Zaag)

• On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow, Analysis and PDE, 2019. (with S. Ibrahim, T. Ghoul)

• Construction of type II blowup solutions for the 1-corotational energy supercritical wave maps, J. Differential Equations, 2018. (with S. Ibrahim, T. Ghoul)

• Construction and stability of blowup solutions for a non-variational semilinear parabolic system, Ann. Inst. H. Poincaré, Anal. non Linéaire, 2018. (with T. Ghoul, H. Zaag)

• Blowup solutions for a reaction-diffusion system with exponential nonlinearities, J. Differential Equations, 2018. (with T. Ghoul, H. Zaag)

• Finite degrees of freedom for the refined blow-up profile for a semilinear heat equation,  Ann. Scient. Éc. Norm. Sup. 2017. (with H. Zaag)

• Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term, J. Differential Equations, 2017. (with T. Ghoul, H. Zaag)

• Numerical analysis of the rescaling method for parabolic problems with blow-up in finite time, Phys. D: Nonlinear Phenomena, 2017.

• Blow-up results for a strongly perturbed semilinear heat equation: Theoretical analysis and numerical method, Analysis and PDE, 2016. (with H. Zaag)