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LIU Bochen

Associate Professor

liubc@sustech.edu.cn

Brief Biography
Research
Teaching
Published Works

Research Interests

Harmonic Analysis, Geometric Measure theory, Combinatorics

Education

2017 Ph.D in Mathematics, University of Rochester, USA

2012 B.S. in Mathematics (Shing-Tung Yau Honor Program), Zhejiang University

Professional Experience

2021.01 - present Associate Professor, Department of Mathematics, Southern University of Science and Technology

2020.11 - 2020.12 Assistant Professor, Department of Mathematics, Southern University of Science and Technology

2020.08 - 2020.11 Visiting Scholar, Department of Mathematics, Southern University of Science and Technology

2019.08 - 2020.07 Postdoc, Mathematics Division, National Center for Theoretical Sciences, Taiwan

2018.08 - 2019.08 Postdoc, Department of Mathematics, Chinese University of Hong Kong

2017.10 - 2018.08 Postdoc, Department of Mathematics, Bar-Ilan University, Israel

2017.07 - 2017.09 Visiting Scholar, Department of Mathematics, Hong Kong University of Science and Technology

2016.10 - 2017.05 Junior Research Assistant, Department of Mathematics, Chinese University of Hong Kong

Representative Publications

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Square function estimates and local smoothing for Fourier integral operators. Proceedings of the London Mathematical Society, 126(2023), 1923–1960.

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Improved local smoothing estimate for the wave equation in higher dimensions. Journal of Functional Analysis, 284(9), 109879.

Iosevich, A., Liu, B., Xi, Y. (2022). Microlocal decoupling inequalities and the distance problem on Riemannian manifolds. American Journal of Mathematics, 144(6), 1601-1639.

Iosevich, A., Lai, C.K., Liu, B., Wyman, E. (2022). Fourier frames for surface-carried measures. International Mathematics Research Notices, 2022(3), 1644-1665.

Liu, B. (2021). Periodic structure of translational multi-tilings in the plane. American Journal of Mathematics, 143(6), 1841-1862.

Lev, N., Liu, B. (2021). Spectrality of polytopes and equidecomposability by translations. International Mathematics Research Notices, 2021(18), 13867-13891.

Lai, C.K., Liu, B., Prince, H. (2021). Spectral properties of some unions of linear spaces. Journal of Functional Analysis, 280(11), 108985.

Liu, B. (2019). An L²-identity and pinned distance problem. Geometric and Functional Analysis, 29(1), 283-294.

Conferences Hosted

1. 2021.09.24 - 2021.09.25 Workshop on Theory and Computation of Partial Differential Equations (SUSTech, Shenzhen)

2. 2021.11.19 - 2021.11.21 Seminars on Harmonic Analysis on Manifolds (SUSTech, Shenzhen)

3. 2022.10.13 - 2022.12.14 Series online reports of Latest Progress on Harmonic Analysis

4. 2023.07.30 - 2023.08.04 Summer School of Fourier Analysis (SUSTech, Shenzhen)

5. 2024.06.21 - 2024.06.25 SUSTech Analysis Workshop 2024 (SUSTech, Shenzhen)

Student Seminar

2022 Fall Riemannian Geometry Seminar

2023 Spring Topics in Analysis

Publications (Last updated: June 2024)

Liu, B. (2024). Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures. Revista Matemática Iberoamericana, 40(2024), 827-858.

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Square function estimates and local smoothing for Fourier integral operators. Proceedings of the London Mathematical Society, 126(2023), 1923–1960.

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Improved local smoothing estimate for the wave equation in higher dimensions. Journal of Functional Analysis, 284(9), 109879.

Iosevich, A., Liu, B., Xi, Y. (2022). Microlocal decoupling inequalities and the distance problem on Riemannian manifolds. American Journal of Mathematics, 144(6), 1601-1639.

Iosevich, A., Lai, C.K., Liu, B., Wyman, E. (2022). Fourier frames for surface-carried measures. International Mathematics Research Notices, 2022(3), 1644-1665.

Liu, B. (2021). Periodic structure of translational multi-tilings in the plane. American Journal of Mathematics, 143(6), 1841-1862.

Lev, N., Liu, B. (2021). Spectrality of polytopes and equidecomposability by translations. International Mathematics Research Notices, 2021(18), 13867-13891.

Liu, B. (2020). On Hausdorff dimension of radial projections. Revista Matemática Iberoamericana, 37(4), 1307-1319.

Lai, C.K., Liu, B., Prince, H. (2021). Spectral properties of some unions of linear spaces. Journal of Functional Analysis, 280(11), 108985.

Liu, B. (2020). Hausdorff dimension of pinned distance sets and the L²-method. Proceedings of the American Mathematical Society, 148(1), 333-341.

Lev, N., Liu, B. (2019). Multi‐tiling and equidecomposability of polytopes by lattice translates. Bulletin of the London Mathematical Society, 51(6), 1079-1098.

Liu, B. (2019). Improvement on 2-chains inside thin subsets of Euclidean spaces. The Journal of Geometric Analysis, 29(4), 3520-3539.

Iosevich, A., Liu, B. (2019). Equilateral triangles in subsets of ℝ^d of large Hausdorff dimension. Israel Journal of Mathematics, 231(1), 123-137.

Liu, B. (2019). Group actions, the Mattila integral and applications. Proceedings of the American Mathematical Society, 147(6), 2503-2516.

Liu, B. (2019). An L²-identity and pinned distance problem. Geometric and Functional Analysis, 29(1), 283-294.

Iosevich, A., Liu, B. (2019). Pinned distance problem, slicing measures, and local smoothing estimates. Transactions of the American Mathematical Society, 371(6), 4459-4474.

Liu, B. (2017). Finite configurations contained in subsets of Euclidean spaces. University of Rochester. (Ph.D. Thesis)

Iosevich, A., Liu, B. (2015). Falconer distance problem, additive energy and Cartesian products. Annales Academiae Scientiarum Fennicae-Mathematica, 41(2), 579–585.

Greenleaf, A., Iosevich, A., Liu, B., Palsson, E. (2015). A group-theoretic viewpoint on Erdős–Falconer problems and the Mattila integral. Revista Matemática Iberoamericana, 31(3), 799-810.

Liu, B. (2014). On radii of spheres determined by subsets of Euclidean space. Journal of Fourier Analysis and Applications, 20(3), 668-678.

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