I am a postdoc in the Department of Mathematics of Uppsala University My advisor is Professor Sunghan Kim and Professor Kaj Nyström.

I got my Bachelor's degree from the University of Science and Technology of China (USTC) in 2022. Then I pursued my Ph.D. for two years at the University of British Columbia (UBC) and transferred to CUHK in my third year (2024) with my supervisor Professor Juncheng Wei. I got my Ph.D. degree in 2026.

Email: zikai.ye@math.uu.se

Address: Ångströmlaboratoriet, Regementsvägen 10, Uppsala, Sweden.

Research Interest

I am interested in constructing solutions to semilinear partial differential equations including the Yamabe Equation, Allen-Cahn equation, (magnetic) Ginzburg-Landau Equation (U(1)-Yang-Mills-Higgs model), and energy-critical heat equation. I am also interested in studying the stability and other properties of these solutions.
I am interested in studying the best constant of some geometric inequalities such as Beckner's inequality, a higher order Moser-Trudinger inequality.

Publications

(With C. Gui, T. Li and J. Wei) A positive answer to the generalized Chang-Yang conjecture on S^N. Preprint, axially-symmetric version.
(With Y. Sire, K. Wu and J. Wei) Giga-Kohn-type results for the fully fractional heat equation. Preprint. Remark.
(With Y. Liu, J. Wei) Stable solutions of U(1)-Yang-Mills-Higgs Model in R^4. Preprint.
(With J. Wei, X. Zeng and Q. Zhang) Co-existence of Type II blow-ups with multiple blow-up rates for five-dimensional heat equation with critical nonlinear boundary conditions. Preprint.
(With C. Gui, T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S^6 and S^8, Advances in Mathematics 480 (2025), part A, Paper No. 110487. Article-Preprint.
(With T. Li and J. Wei) On sharp Beckner’s inequality for axially symmetric functions on S^4, Math Research Letters 31(2024), no.5, 1523-1550. Article-Preprint.
(With J. Andrade and J. Wei) Complete metrics with constant fractional higher order Q-curvature on the punctured sphere, The Journal of Geometric Analysis, 2023, 34(1), 6. Article-Preprint.
(With R.Lyu) 2D Thin obstacle problem with data at infinity. Preprint.

Invited talks

Stable solutions to the U(1)-Yang-Mills-Higgs model.

Aug 19, 2026, at Workshop on Nonlinear PDEs, Harmonic Analysis and FBPs, KTH.

Stability of solutions to the U(1)-Yang-Mills-Higgs equation in R^4.

Jan 15, 2025, at National University of Singapore.

On sharp Beckner’s inequality for axially symmetric functions on S^4, S^6 and S^8.

June 1, 2024, at Scholars Symposium on Nonlinear Analysis at Wuhan University of Technology.

On sharp Beckner’s inequality for axially symmetric functions on S^4 and S^6.

Nov 3, 2023, at Ming Li Colloquium at Wuhan University of Technology.

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