Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
Title: Assistant Professor
Office: Room 315, Run Run Shaw Building
Phone: (852) 39171997
Email: xz27 [AT] hku.hk
mathzhangxin [AT] gmail.com
Embedded Files
Research interests: Number Theory, Arithmetic Combinatorics, Dynamical Systems
Teaching:
Fall 2024, Math 3401 Analysis I
Fall 2024, Math 1851 Calculus and Ordinary Differential Equations
Publications:
Sum-product Phenomenon in Quotients of Rings of Algebraic Integers (with J. Tang), accepted, Journal d'Analyse Mathématique (2025).
On the local-global conjecture for combinatorial period lengths of closed billiards on the regular pentagon (with A. Kontorovich), accepted, International Mathematics Research Notices (2024).
On length sets of subarithmetic hyperbolic manifolds (with A. Kontorovich), Mathematische Annalen 2024-07, Vol.389 (3), p.2783-2855
Logarithmic bounds for the diameters of some Cayley graphs (with L. Pham), Journal of Group Theory, Volume 25, No. 2, 2022, Pages 327-342.
Statistical regularity of Apollonian gaskets, International Mathematics Research Notices, Volume 2021, Issue 2, January 2021, Pages 1055-1095.
Inducing super-approximation (with A. Salehi-Golsefidy), International Mathematics Research Notices, Volume 2021, Issue 14, July 2021, Pages 10442-10468.
Local-global principles in circle packings (with E. Fuchs and K. Stange), Compositio Mathematica, 155.6 (2019), Pages 1118-1170.
Spatial statistics of Apollonian gaskets (with W. Chen, M. Jiao, C. Kessler and A. Malik), Experimental Mathematics. 28.3 (2019), Pages 263-270.
On representation of integers from thin subgroups of SL(2, Z) with parabolics, International Mathematics Research Notices, Volume 2020, Issue 18, September 2020, Pages 5611-5629.
The gap distribution of directions in some Schottky groups, Journal of Modern Dynamics, 11 (2017), 1930-5311.
Gap distributions in circle packings (with Z. Rudnick), Münster Journal of Mathematics 10 (2017), 131-170.
On the local-global principle for integral Apollonian 3-circle packings. Journal für die reine und angewandte Mathematik (Crelle's journal) 2018.737 (2018): 71-110
Preprints:
Super Approximation for SL2 × SL2 AND SL2 semidirect ASL2 (with J. Tang), preprint (2023).
An asymptotic local-global theorem on heights of some Kleinian group orbits (with X. Xiao), preprint (2024).
Lecture Notes:
Sum-product, super approximation and local-global phenomenon in thin groups, Summer School on Analytic Number Theory, June 09-20, 2025, iHarbour Campus, Xi'an Jiaotong University
Page updated
Google Sites
Report abuse