Research

I am interested in anything that is related to PDEs.

Topics that I have been looking at recently include: probabilistic theory of PDEs, wave turbulence and kinetic theory, statistical physics and quantum field theory, inviscid and Landau damping.

Topics that I may be looking at in the future include: random geometry, formation and non-formation of singularity, infinite dimensional KAM theory.

Selected Papers (full publication list):

Kinetic theory / Wave turbulence:

• Y. Deng, Z. Hani and X. Ma. Long time derivation of Boltzmann equation from hard sphere dynamics. arXiv:2408.07818.

• Y. Deng and Z. Hani. Long time justification of wave turbulence theory. arXiv:2311.10082.

• Y. Deng and Z. Hani. Full derivation of the wave kinetic equation. Invent. Math. 233 (2023), no. 2, 543–724.

Notes on the long-time derivation of Boltzmann: 

• Expository notes: Overview of the proof (surveys the main ingredients of the proof), Toy model algorithms (explains the cutting algorithm with full details in a simplified setting)

• PKU lecture series: Lecture 1, Lectures 2-3, Lecture 4, Lecture 5 (please note there might be minor notational differences between the notes and the actual lectures)

Probabilistic PDEs:

• B. Bringmann, Y. Deng, A. Nahmod and H. Yue. Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation. Invent. Math. 236 (2024), no. 3, 1133–1411.

• Y. Deng, A. Nahmod and H. Yue. Random tensors, propagation of randomness, and nonlinear dispersive equations. Invent. Math. 228 (2022), no. 2, 539–686.

• Y. Deng, A. Nahmod and H. Yue. Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two. Ann. of Math. (2) 200 (2024), no. 2, 399–486.

Miscellaneous:

• Y. Deng and N. Masmoudi. Long time instability of the Couette flow in low Gevrey spaces. Comm. Pure Appl. Math. 76 (2023), no. 10, 2804–2887.

• Y. Deng. On growth of Sobolev norms for energy critical NLS on irrational tori: Small energy case. Comm. Pure Appl. Math. 72 (2019), no. 4, 801–834.

• Y. Deng, A. Ionescu, B. Pausader and F. Pusateri. Global solutions of the gravity-capillary water wave system in three dimensions. Acta Math. 219 (2017), no. 2, 213–402.