Bochen Liu
Associate Professor
Research interest: Harmonic Analysis， Geometric Measure，Theory Combinatorics

#### Research Interests：

Harmonic Analysis

Geometric Measure Theory

Combinatorics

#### Working Experience：

Southern University of Science and Technology, Shenzhen, China

Associate Professor January 2021 – present

Assistant Professor November 2020 – December 2020

Visiting Scholar August 2020 – November 2020

National Center for Theoretical Sciences, Taiwan

Postdoc August 2019 – July 2020 • Mentor: Chun-Yen Shen •

Entry banned since January 26 2020

Chinese University of Hong Kong Postdoc

August 2018 – August 2019 • Mentor: Po-Lam Yung

Bar-Ilan University, Israel Postdoc

October 2017 – August 2018 • Mentor: Nir Lev

Hong Kong University of Science and Technology

Visiting Scholar July 2017 – September 2017

Chinese University of Hong Kong Junior

Research Assistant October 2016 – May 2017 • Mentor: Ka-Sing Lau

Publication (accepted and above)：

1. On radii of spheres determined by subsets of Euclidean space, J. Fourier Anal. Appl. 20 (2014), no.3, 668-678.

2. A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral (with Allan Greenleaf, Alex Iosevich, Eyvindur A. Palsson), Rev. Mat. Iberoam. 31 (2015), no.3, 799- 810.

3. Falconer distance problem, additive energy and Cartesian products (with Alex Iosevich), Ann. Acad. Sci. Fenn. Math. 41 (2016), no.2, 579-585.

4. Equilateral triangles in subsets of R d of large Hausdorff dimension (with Alex Iosevich), Israel J. Math. 231 (2019), no.1, 123-137.

5. Group actions, the Mattila integral and applications, Proc. Amer. Math. Soc. 147 (2019), no.6, 2503-2516.

6. Pinned distance problem, slicing measures, and local smoothing estimates (with Alex Iosevich), Trans. Amer. Math. Soc. 371 (2019), no.6, 4459-4474.

7. Improvement on 2-chains inside thin subsets of Euclidean spaces, J. Geom. Anal. 29 (2019), no.4, 3520-3539.

8. An L 2 -identity and pinned distance problem, Geom. Funct. Anal. 29 (2019), no.1, 283-294.

9. Multi-tiling and equidecomposability of polytopes by lattice translates (With Nir Lev), Bull. Lond. Math. Soc. 51 (2019), no.6, 1079-1098.

10. Periodic structure of translational multi-tilings in the plane, Amer. J. Math. 143 (2021), no.6, 1841-1862.

11. Hausdorff dimension of pinned distance sets and the L 2 - method, Proc. Amer. Math. Soc. 148 (2020), no.1, 333-341.

12. Spectrality of polytopes and equidecomposability by translations (with Nir Lev), Int. Math. Res. Not. IMRN 2021, no.18, 13867- 13891.

13. On Hausdorff dimension of radial projections, Rev. Mat. Iberoam., 37 (2021), no.4, 1307-1319.

14. Fourier frames for surface-carried measures (with Alex Iosevich, Chun-Kit Lai, Emmett Wyman), Int. Math. Res. Not. IMRN 2022, no.3, 1644-1665,

15. Microlocal decoupling inequalities and the distance problem on Riemannian manifolds (with Alex Iosevich, Yakun Xi), Amer. J. Math., accepted for publication, arXiv:1909.05171.

16. Spectral properties of some unions of linear spaces (with Chun-Kit Lai, Hal Prince), J. Funct. Anal. 280 (2021), no.11, 108985.