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
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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:
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:
Sum-product Phenomenon in Quotients of Rings of Algebraic Integers (with J. Tang), preprint (2023).
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).
On the local-global conjecture for combinatorial period lengths of closed billiards on the regular pentagon (with A. Kontorovich), preprint (2024).
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