Shao Liu

I am a fourth-year PhD student at the Mathematical Institute of the University of Bonn, under the supervision of Prof. Dr. Herbert Koch and Prof. Tadahiro Oh.

Research Interests:

Nonlinear partial differential equations and harmonic analysis. In particular, I have been focusing on (deterministic and probabilistic) dispersive PDEs using tools from PDEs, harmonic analysis, and probability theory.

My CV can be found here (last update in October 2025).

E-mail: shaoliu@math.uni-bonn.de

Office: Room N2.008, Endenicher Allee 60, University of Bonn

Research

Publications

(with G. Li, J. Li, T. Oh, and N. Tzvetkov) Probabilistic well-posedness of dispersive PDEs beyond variance blowup II: quadratic nonlinear wave equation, in preparation.
(with D. Greco and T. Oh) Global well-posedness for the modulated Korteweg-de Vries equation in negative Sobolev spaces, in preparation.
(with R. Liu and T. Oh) Hyperbolic O(N) linear sigma model and its mean-field limit, in preparation.
(X. Nie, D. Yan, and Y. Deng) Rearrangement inequality for Hardy-Littlewood maximal operator. Banach J. Math. Anal. 16 (2022), no. 3, Paper No. 43, 30 pp.

Talks

(Upcoming) Analysis Seminar, ENS Lyon, Lyon, France, 19 Jan. 2026.
(Upcoming) SFB Seminar, University of Bonn, Bonn, Germany, 13 Jan. 2026.
(Upcoming, Poster) 2nd Atlantic Conference in Nonlinear PDEs, Instituto Superior Técnico - University of Lisbon, Lisbon, Portugal, 3-7 Nov. 2025.
Analysis Seminar, The University of Edinburgh, Edinburgh, UK, 29 Sept. 2025.
Arbeitsgemeinschaft: Quantum Signal Processing and Nonlinear Fourier Analysis, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, 6-11 Oct. 2024.
(Short Talk) Oberwolfach Seminar: Recent Topics on the Navier-Stokes Equations, Oberwolfach, Germany, 22-27 Oct. 2023.
Analysis Seminar, Institute of Mathematics, Chinese Academy of Sciences, Beijing, China, 10 Aug. 2023.

Teaching

University of Bonn, Germany

Winter term 25/26, Graduate Seminar on Advanced Topics in PDE

University of Chinese Academy of Sciences, China

Spring 2021, Tutor for "Calculus II"
Autumn 2020, Tutor for "Real Analysis"

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