研究方向
调和分析、几何测度论、组合数学
教育经历
2017 美国罗切斯特大学数学博士
2012 浙江大学数学学士（丘成桐数学英才班）
工作经历
2021.01 - 南方科技大学数学系副教授
2020.11 - 2020.12 南方科技大学数学系助理教授
2020.08 - 2020.11 南方科技大学数学系访问学者
2019.08 - 2020.07 台湾大学理论科学研究中心数学部博士后
2018.08 - 2019.08 香港中文大学数学系博士后
2017.10 - 2018.08 以色列巴伊兰大学数学系博士后
2017.07 - 2017.09 香港科技大学数学系访问学者
2016.10 - 2017.05 香港中文大学数学系研究助理
代表文章
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.
会议主持
1. 2021.09.24 - 2021.09.25 偏微分方程理论与计算研讨会（南方科技大学，深圳）
2. 2021.11.19 - 2021.11.21 流形上的调和分析学术交流会（南方科技大学，深圳）
3. 2022.10.13 - 2022.12.14 “调和分析最新进展”系列线上报告
4. 2023.07.30 - 2023.08.04 傅里叶分析暑期研讨会（南方科技大学，深圳）
5. 2024.06.21 - 2024.06.25 南方科技大学分析研讨会2024（南方科技大学，深圳）
学生讨论班
2022秋季 黎曼几何讨论班
2023春季 分析专题
学术成果 (更新时间：2024年6月）
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 ℝd 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.
