Guopeng Li

I am a Maxwell Institute Postdoctoral Research Fellow in Edinburgh.

I completed my PhD at the University of Edinburgh (MIGSAA CDT) under the supervision of Prof. Tadahiro Oh and Prof. Yuzhao Wang.

My thesis can be found here: Deep-water and shallow-water limits of the intermediate long wave equation: from deterministic and statistical viewpoints

Research Interests:

Nonlinear Partial Differential Equations and Harmonic Analysis. In particular, study of (deterministic and probabilistic) nonlinear dispersive PDEs.

I am also interested in completely integrable models. Moreover, I have broadened my interests in probability theory through chatting with Guangqu Zheng (Liverpool).

Non-maths Interests:

I regularly work out at the gym, and occasionally train with Hiro to maintain our powerlifting records. While Guangqu was in Edinburgh, we used to work out together and explore various restaurants.

preprints on arXiv

(with Á. Bényi, R.H. Torres, T.Oh) Compact T(1) theorem à la Stein.
(with Á. Bényi, R.H. Torres, T. Oh) Compact bilinear operators and paraproducts revisited.
(with J. Forlano, T. Zhao) Unconditional deep-water limit of the intermediate long wave equation in low-regularity.
(with L. Tao, T. Zhao) Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation.
(with A. Chapouto, T. Oh) Deep-water and shallow-water limits of statistical equilibria for the intermediate long wave equation.
(with A. Chapouto, J. Forlano, T. Oh, D. Pilod) Intermediate long wave equation in negative Sobolev spaces, to appear in Proc. Amer. Math. Soc. Ser. B.
(with A. Chapouto, T. Oh, D. Pilod) Deep-water limit of the intermediate long wave equation in L².
(with E. Brun, R. Liu) Global well-posedness of the energy-critical stochastic nonlinear wave equations, J. Differential Equations 397 (2024), 316--348.
(with E. Brun, R. Liu, Y. Zine) Global well-posedness of the one-dimensional fractional cubic nonlinear Schrödinger equations.
(with R. Liang, Y. Wang) Optimal divergence rate of the focusing Gibbs measure.
(with A. Chapouto, R. Liu) Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus.
(with T. Oh, G. Zheng) On the deep-water and shallow-water limits of the intermediate long wave equation from a statistical viewpoint.
Deep-water and shallow-water limits of the intermediate long wave equation.
(with K. Cheung) Global well-posedness of the 4-d energy-critical stochastic NLS with non-vanishing boundary condition, Funkcial. Ekvac. 65 (2022), no. 3, 287--309.
(with K. Cheung, T. Oh) Almost conservation laws for stochastic nonlinear Schrödinger equations, J. Evol. Equ. 21 (2021), 1865--1894.

Talks:

Short visit at Institute for Mathematics - TU Clausthal, Germany, June 10, 2024.
Edinburgh Analysis Seminar, University of Edinburgh Edinburgh, UK, February 5, 2024.
(Poster) Seminar series on Probability, Stochastic Analysis and Mathematical Finance, Shanghai Jiao Tong University, Shanghai, China, December 27, 2023.
Numerical and analytical approaches for nonlinear dispersive PDEs, Institut de Mathématiques de Bourgogne (IMB), Dijon, France, November 27-30, 2023.
Analysis seminar, Morningside center of mathematics, Chinese Academy of Sciences, Beijing, China, October 26, 2023.
Analysis seminar, ShanghaiTech University, Shanghai, China, October 23, 2023.
Analysis seminar, Capital Normal University, Beijing, China, October 19, 2023.
Analysis seminar, Institute of Applied Physics and Computational Mathematics, Beijing, China, October 18, 2023.
Analysis seminar, Beijing Institute of Technology, Beijing, China, October 17, 2023.
Mini-symposium "Cauchy problem for deterministic and stochastic nonlinear dispersive equations" at 10th ICIAM, Waseda University, Tokyo, Japan, August 20-25, 2023.
Random dispersive PDEs 2023, University of Birmingham, Birmingham, UK, July 19-21, 2023.
Seminar talk at Institute for Mathematics - TU Clausthal, Germany, June 19, 2023.
(co-organizer and speaker) Deterministic and Probabilistic Dynamics of Nonlinear Dispersive PDEs, Maxwell Institute, Edinburgh, UK, June 14-16, 2023.
Junior Analysis and Probability Seminar, University of Warwick, UK, Feb. 2023.
APDE Webinar, China, Jan. 2023.
Workshop: Stochastics and nonlinear partial differential equations, Osaka University, Japan, Dec. 2022.
NLPDE Seminar, Kyoto University, Japan, Dec. 2022.
Special Analysis Seminar, Chuo University, Tokyo, Japan, Nov. 2022.
104th Analysis Seminar, Saitama University, Japan, Nov. 2022.
One-day workshop on nonlinear stochastic PDE, Keio University, Tokyo, Japan, Nov. 2022.
(Poster) Trials in Wave Turbulence: from random waves to kinetic equations, Gran Sasso Science Institute, L'Aquila, Italy, September 5-10, 2022.
One-day workshop on Probabilistic aspects of nonlinear dispersive equations, University of Birmingham,UK, July. 2022.
"Harmonic Analysis, Stochastics and PDEs" in Honor of the 80th Birthday of Nicolai Krylov, ICMS, Edinburgh, UK, June 20-24, 2022.
Dispersive Day 2022, The Maxwell Institute for Mathematical Sciences, Edinburgh, UK, June. 2022.
Virtual Maxwell Analysis seminar, The Maxwell Institute for Mathematical Sciences, Edinburgh, UK, June. 2020.
Nonlinear and stochastic partial differential equations, Research Institute for Mathematical Sciences, Kyoto, Japan, Nov. 2019.

Conference participation:

Conference "IMS Anniversary Symposium on PDEs" Institute of Mathematical Science, Shanghai, China, October 21 - 22, 2023.
Conference "Water Waves and Integrable Systems" Order and Randomness in Partial Differential Equations, Institute Mittag-Leffler, Sweden, September 11 - 15, 2023.
Conference "Harmonic Analysis and Partial Differential Equations" - 60th birthday of Herbert Koch, Hausdorff Center for Mathematics, Bonn, Germany, May - Jun. 2023.
Hamiltonian Methods and Asymptotic Dynamics, Hamiltonian Methods in Dispersive and Wave Evolution Equations, ICERM, Brown University, Providence, RI, USA, Dec. 2021.
Convex Integration and Nonlinear Partial Differential Equations, International Centre for Mathematical Sciences, Edinburgh, UK, November 08-12, 2021.
(online) Analysis Seminar, Peking University, Peking University, China, Oct. 20&27, Nov. 03, 2021.
(online) Evolution Equations in Mathematical Physics: Dispersive and Hyperbolic, Tianjin University, China, Sep. 2021.
(online) Bath Mathematical Symposium on "PDE and Randomness" University of Bath, UK, Sep. 2021.
"Harmonic Analysis and Nonlinear Partial Differential Equations", Research Institute for Mathematical Sciences, Kyoto, Japan, Jun. 2021.
Summer School "New Frontiers in Singular SPDEs and Scaling Limits", Hausdorff Research Institute for Mathematics, Bonn, Germany, September 23-27, 2019.
MIGSAA 5th Annual Colloquium, ICMS, Edinburgh, UK, September 20, 2019.
Summer School in Analysis of PDEs and Fluid Dynamics, Edinburgh, UK, July 23-26, 2019.
Dispersive Waves and Related Topics: a conference in honor of Gilles Lebeau, Bergen, Norway, June 17-21, 2019.
MIGSAA 4th Annual Colloquium, ICMS, Edinburgh, UK, September 21, 2018.

Project supervision

Fall 2023 - Spring 2024:	Standing waves for the nonlinear Schrödinger equation (Undergraduate project)
Fall 2022 - Spring 2023:	Standing waves for the nonlinear Schrödinger equation (MMath dissertation)

Lecturer/Teaching assistant

Spring (2023-UoE):	Lecturer for Honours Algebra -Workshops for Honours Algebra and Algebra-Skills (programming)
Fall (2022-UoE):	Lecturer (joint with Ivan Cheltsov) for Accelerated Algebra and Calculus for Direct Entry -Workshops for Accelerated Algebra and Calculus for Direct Entry
Spring (2022-UoE):	Workshops for Engineering Mathematics 1a/Natural Sciences 1a Workshops for Fundamentals of Pure Mathematics
Fall (2021-UoE):	Workshops for Accelerated Algebra and Calculus for Direct Entry Workshops for Introduction to Linear Algebra Nonlinear Schrödinger Equations
Spring (2021-UoE):	Workshops for Engineering Mathematics 1b/Natural Sciences 1b
Fall (2020-UoE):	Workshops for Engineering Mathematics 1a/Natural Sciences 1a
Spring (2020-UoE):	Workshops for Introduction to Number Theory Workshops for Nonlinear Schrödinger Equations
Fall (2019-UoE):	MathsBase, Workshops for Honours of Analysis Workshops for Engineering Mathematics 1a/Natural Sciences 1a Workshops for Introduction to Data Science

Academic Positions

Sep. 2022 -

Postdoctoral Fellow, Maxwell Institute, UK

Education:

Sep. 2018 - Aug. 2022	Ph.D. in Mathematics , University of Edinburgh, UK - Supervisors: Tadahiro Oh & Yuzhao Wang
Sep. 2017 - Aug. 2018	MSc. in Mathematics, University of Warwick, UK - Supervisor: Vedran Sohinger
Sep. 2014 - Aug. 2017	BSc. in Mathematics, University of Sheffield, UK - Tutor: Caitlin Buck

Student supervision:

Sep. 2023 - Mar. 2024	Ziqian Fang, University of Edinburgh, UK
Sep. 2022 - Mar. 2023	Yan Ding, University of Edinburgh, UK - Ph.D. candidate at HKUST (Guangzhou)

Awards:

Apr. 2024	"Supervisor of the Year", University of Edinburgh
Apr. 2023	"Supervisor of the Year", University of Edinburgh
Mar. 2022	Laura Wisewell Travel Scholarship
Apr. 2022	"Student Tutor of the Year", University of Edinburgh
Sep. 2018- Aug. 2023	EPSRC Ph.D funding
Sep. 2017- Aug. 2018	Master scholarship funding
Sep. 2014- Aug. 2017	Undergraduate academic excellence funding

Notes:

(2019) Stochastic nonlinear dispersive PDEs - MIGSAA Extended Project report
(2018) Well-posedness theory for the nonlinear Schrödinger equation - MSc. dissertation

Li, Guopeng (李國鵬)