Xin Zhang 张欣

About Me

I am a postdoc at Institut des Hautes Études Scientifiques.

From September 2015 to October 2018 I was a Doob Assistant Professor at University of Illinois of Urbana-Champaign.

From July 2014 to July 2015 I was a postdoc at Tel Aviv University.

From September 2009 to May 2014, I was a PhD student of Alex Kontorovich at Stony Brook University.

Research interests

analytic number theory, hyperbolic geometry, homogeneous dynamics, linear algebraic groups.

Papers and preprints

For the link to my papers on arXiv, click here .

1. Statistical regularity of Apollonian gaskets, 2017(pdf)
   Accepted by International Mathematial Research Notices
2. Inducing super-approximation, 2017 (pdf)
   (with Alireza Salehi-Golsefidy) Submitted
3. Local to global principles in circle packings, 2017 (pdf)
   (with Elena Fuchs and Kate Stange) Accepted by Compositio Math
4. Spatial statistics of Apollonian Gaskets, 2017 (pdf)
   (with Weiru Chen, Mo Jiao, Calvin Kessler and Amita Malik)
   Accepted by Experimental Mathematics
5. On representation of integers from thin subgroups of SL(2, Z) with parabolics, 2016 (pdf)
   Accepted by International Mathematical Research Notices
6. The gap distribution of directions in some Schottky groups, 2015 (pdf)
   Journal of Modern Dynamics VOLUME 11, 2017, 477–499
7. Gap Distributions in Circle Packings, 2015 (pdf)
   (with Zeev Rudnick) Münster Journal of Mathematics 10 (2017), 131–170
8. On the local-global principle for integral Apollonian-3 circle packings, 2014 (pdf)
   Journal für die reine und angewandte Mathematik (Crelle’s Journal) ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, August 2015 pp. 1219–1224

Mentoring

In Spring 2017, I mentored the following three Illinois geometry lab (IGL) undergraduate research projects:

• Geometry of Apollonian circle packings (poster, paper)
  Undergraduate investigators: Weiru Chen, Mo Jiao, Calvin Kessler
  Graduate mentor: Amita Malik
• Finding integers from group orbits (poster)
  Undergraduate investigators: Jake Shin, Yike Xu, Catherine Zhang, Xin Zhang
  Graduate mentor: Junxian Li
• Self-Intersection Numbers of Closed Geodesics in Infinite Volume Hyperbolic Surfaces (poster)
  Undergraduate investigators: Yujia Yan, Peiwen Zhang, Xianhao Zhang
  Graduate mentor: Hadrian Quan

Expository: informal notes, slides, and letters

• Slides for my two talks given at Yale, on the geometric and number theoretic aspects of circle packings, 2017 (talk1,talk2)
• A short note on a theorem of Mohammadi-Oh, 2017 (pdf)
• Slides for the Doob Colloquium talk at UIUC, 2017 (pdf)
• Slides for the UC Davis talk on the gap distribution of thin Schottky group orbits, 2016 (pdf)
• Slides for the Dead Sea talk on the gap distribution of circle packings, 2015 (pdf)
• A dynamical outlook on orbital counting problems (pdf)
  (with Claire Burrin) Summery written for the EWM summer school on Apollonian circle packings, 2014