Zhiqiang Li
Beijing, China
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Office
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BICMR 78105W-1
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Office Hours
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By appointment
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E-Mail
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zli at math .pku .edu .cn
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Research
Interests
My
research interests lie in the interplay of dynamical systems and geometry of
spaces with fractal nature.
Positions
I got my PhD in 2015 from UCLA under the
supervision of Professor Mario Bonk.
Before joining Peking University in Fall 2019, I was a postdoc as a Milnor
Lecturer at the Institute for
Mathematical Sciences at Stony Brook
University, under the supervision of Professor Misha Lyubich during Fall
2015 and from Fall 2016 to Spring 2019. From February to May 2016, I was a
Semester Postdoctoral Research Fellow at the Institute for Computational and
Experimental Research in Mathematics (ICERM) at Brown
University under the supervision of Professor Katrin Gelfert. I got my Master’s and Bachelor’s degrees from the
University of Toronto under the supervision of Professor Ilia Binder and Charles C. Pugh,
respectively.
Teaching
Fall 2025: Ergodic Theory (taught in English)
Spring 2026: Dynamical Systems
Conferences & Summer/Winter Schools
May 20–23, 2025: Sino-Uzbeki
Conference on Complex Analysis (organized by Gang Tian, Xiaobo Liu, Zhiqiang Li, Hanlong Fang; Sadullaev, Abdullaev, Eshmetov,
Ibragimov, etc.)
April 24–25, 2025: International
Symposium on Dynamical Systems (organized by Zhiqiang Li, Misha Lyubich, and Ke Zhang; featuring Avila, De Simoi, Kaloshin,
Kanigowski, Xie, and Yampolsky)
Seminars
Pacific Quasiworld
(organized by Mario Bonk, Yunping Jiang, Zhiqiang Li, and Mitsuhiro
Shishikura)
The Long Run—Topics in Ergodic Theory
(organized by Ilia Binder, Jacopo De Simoi, Zhiqiang Li, Federico
Rodriguez-Hertz, and Mariusz Urbański)
Advances in Dynamics Seminar (organized by Zhiqiang
Li, Misha Lyubich, and Michael Yampolsky)
Undergraduate 3+X Complex Analysis & Complex Dynamics Seminar - Complex
Analysis, Geometry, and Dynamics (Fall 2022 - current) (PKU, organized by Zhiqiang Li)
Prof. Wen’s seminar (PKU)
Past
Seminars
Undergraduate
Dynamics Seminar (Spring 2022) (PKU,
organized by Wenyuan Yang and Zhiqiang Li)
Undergraduate
Dynamics Seminar (Fall 2020 - Spring 2021) (PKU, organized by Shaobo Gan, Disheng Xu, and Zhiqiang Li)
Visitors and Mini-courses (in person)
May 17 – June 11 2023 Kasra
Rafi (University of Toronto, Canada)
June 3–13 2023 Mario Bonk (UCLA, USA)
July 14–15 2023 Dylan Thurston
(Indiana University, USA)
August 23 – September 7 2023 Tianyi
Zheng (UCSD, USA)
September 6–11 2023 Oliver Jenkinson
(Queen Mary, University of London, UK)
October 9–18 2023 Ilia
Binder (University of Toronto, Canada)
January 6–14 2024 Pekka
Pankka (University of Helsinki, Finland)
March 25–29 2024 Yunping
Jiang (City University of New York, USA)
April 21–May 4 2024 Daniel
Meyer (University of Liverpool, UK)
August 25–30 2024 Mario Bonk (UCLA, USA)
August 25–31 2024 John
Erik Fornæss (University of Michigan, Norwegian University of Science and
Technology)
August 24–30 2024 Pekka
Pankka (University of Helsinki, Finland)
September 15–19 2024 Polina Vytnova
(University of Surrey, UK)
September 17–24 2024 Mark
Pollicott (University of Warwick, UK)
October 5–7 2024 LING San
(Nanyang Technological University, Singapore)
December 14–23 2024 Eero Saksman
(University of Helsinki, Finland)
January 11–25 2025 Walter
Bergweiler (Christian-Albrechts-Universität zu Kiel,
Germany)
January 11–25 2025 Daniel
Meyer (University of Liverpool, UK)
January 13–25 2025 Sergiy Merenkov (City
University of New York, USA)
January 16–25 2025 Yunping
Jiang (City University of New York, USA)
February 16–25 2025 Sylvester
Eriksson-Bique (University of Jyväskylä, Finland)
May 8–11 2025 DINH Tien-Cuong (National
University of Singapore)
May 8–11 2025 Fabrizio Bianchi
(University of Pisa, Italy)
June 23–26 2025 WU Guohua
(Nanyang Technological University, Singapore)
August 13–14 2025 Vadim
Kaloshin (Institute of Science and Technology Austria)
September 1–10 2025 Sabyasachi Mukherjee (Tata Institute of
Fundamental Research, India)
September 8–14 2025 Sylvester
Eriksson-Bique (University of Jyväskylä, Finland)
September 11–20 2025 Mario Bonk (UCLA, USA)
September 12–20 2025 Lukas Geyer (Montana State
University, USA)
October 24–November 4 2025 William Verreault (University of
Toronto, Canada)
November 6–19 2025 Roland Roeder
(Indianapolis University, USA)
December 19–24 2025 Yan Mary He (University of
Oklahoma, USA)
Publications
and Preprints
² Z. Li
(with Ranfeng
Yu, Tianyi
Zheng), Quasi-isometric rigidity for random
subsets in product of trees.
² Z. Li
(with Zelai Hao, Yinying
Huang, Oliver Jenkinson), Joint
typical periodic optimization: systems with stable hyperbolicity. Submitted, (arXiv:2605.01550). 33
pages. (PDF)
² Z. Li
(with Yinying
Huang,Oliver Jenkinson), Ergodic
optimization for Gauss’s continued fraction map. Submitted, (arXiv: 2512.21394). 42 pages. (PDF)
² Z. Li
(with Xianghui
Shi), Counting prime orbits in shrinking intervals
for expanding Thurston maps. Submitted, (arXiv: 2511.22601). 33 pages. (PDF)
² Jie Yan†,
Maolin Wang†, Junzhong Xie†, Yapeng Zhao†, Xianghui Shi†, Yuxiong Hu,
Shixiang Yu, Xingwu Liu, Mingyu Chu, Jie Zhang, Chaowu Xue, Shuheng Tian,
Yaxuan Wang, Zijun Peng, Wu Zhou, Hiroyuki Asakura, Meng Wang, Zhiqiang Li*,
Zhu-Jun Wang*, Ding Ma*, Reactive Oxygen
Pool over Ceria Enables Catalytic Oscillation. Submitted, (10.21203/rs.3.rs-9275333/v1). (†:
First authors; *: communication authors.) (PDF)
² Z. Li
(with Hanyun
Zheng), A class of Lattès maps with
cellular structures. Submitted, (arXiv: 2512.00372). 16 pages. (PDF)
² Z. Li
(with Pekka
Pankka, Hanyun
Zheng), Rigidity and quasisymmetric uniformization of
Thurston-type maps. Submitted, (arXiv: 2501.00434). 53 pages. (PDF)
² Z. Li
(with Nils
Hemmingsson, Xiaoran Li), Conformal measures of
(anti)holomorphic correspondences. Submitted, (arXiv: 2409.01361). 37 pages.
(PDF)
² Z. Li
(with Ilia
Binder, Qiandu He, Xianghui Shi), Computable
thermodynamic formalism. Submitted, (arXiv: 2512.01259). 39 pages. (PDF)
² Z. Li
(with Yiqing Sun), Tropical
thermodynamic formalism. Adv. Math. 491 (2026), 110864. 69 pages. (PDF)
² Z. Li
(with Ruicen Qiu), General harmonic measures for
distance-expanding dynamical systems. Submitted, (arXiv:2405.02987). 44 pages. (PDF)
² Z. Li
(with Xianghui
Shi), Entropy density and
large deviation principles without upper semi-continuity of entropy. Submitted, (arXiv:2406.01712). 59 pages. (PDF)
² Z. Li
(with Xianghui
Shi), Thermodynamic
formalism for subsystems of expanding Thurston maps II. Submitted, (arXiv:2404.07247). 46 pages. (PDF)
² Z. Li
(with Xianghui
Shi, Yiwei Zhang), Thermodynamic
formalism for subsystems of expanding Thurston maps and large deviations
asymptotics. Proc. Lond. Math.
Soc. (3) 130, 2025, e70019. 77
pages. (PDF)
² Z. Li
(with Xiaoran Li, Yiwei
Zhang), Thermodynamic
formalism for correspondences. Submitted, (arXiv: 2311.09397). 49 pages.
(PDF)
² Z. Li
(with Hanyun
Zheng), Weak expansion
properties and a large deviation principle for coarse expanding conformal
systems. Int. Math. Res. Not. IMRN 2025 (2025),
rnaf046. 31 pages. (PDF)
² Z. Li
(with Jian Ding, Yiwei
Zhang), On the prevalence of
the periodicity of maximizing measures. Adv. Math. 438 (2024), 109485. 23 pages.
(PDF)
² Z. Li
(with Yiwei
Zhang), Ground states and
periodic orbits for expanding Thurston maps. Math. Ann., 391 (2025), 3913–3985. 73
pages. (PDF)
² Z. Li
(with Tianyi
Zheng), Prime orbit theorems
for expanding Thurston maps: Genericity of strong
non-integrability condition. Adv. Math. 450 (2024), 109765. 32 pages. (PDF)
² Z. Li
(with Tianyi
Zheng), Prime orbit theorems
for expanding Thurston maps: Lattès maps and split Ruelle operators. Adv. Math. 449 (2024), 109723. 96 pages. (PDF)
² Z. Li
(with Tianyi
Zheng), Prime orbit theorems
for expanding Thurston maps: Dirichlet series and orbifolds. Adv. Math. 443 (2024), 109600. 89 pages. (PDF)
² Z. Li, Ergodic theory of expanding Thurston maps,
volume 4 of The
Atlantis Series in Dynamical Systems, Atlantis
Press (Springer), 2017. 191 pages. (PDF)
² Z. Li,
Weak expansion properties and large deviation principles for expanding Thurston
Maps. Adv. Math. 285 (2015), 515
–567. (PDF)
² Z. Li,
Equilibrium states for expanding Thurston maps. Comm. Math. Phys. 357 (2018), 811–872.
(PDF)
² Z. Li,
Periodic points and the measure of maximal entropy of an expanding Thurston
map. Trans. Amer. Math.
Soc., 368 (2016), 8955–8999. (PDF)
² Z. Li
(with Balasingham Balamohan and Stephen Tanny), A Combinatorial Interpretation for Certain
Relatives of the Conolly Sequence. J. Integer Seq., 11 (2008), Article
08.2.1. (PDF).
Past and
Current Postdocs
3.
Chengliang Tan, 2025 - current
Student
Research
Graduate Students
Hongfei Liu graduated with a Master's degree in 2023 and
worked with me on local central limit theorems for topological Collet–Eckmann maps.
Yinying Huang has been working with me on the Typically
Periodic Optimization Conjecture in a countable setting. A manuscript is in
preparation. Yinying has also been working with Zelai Hao and me on the
Typically Periodic Optimization Conjecture for the β-transformations. He is also interested in topological
Collet-Eckmann maps and random dynamical systems.
Xianghui Shi has been working with me and Yiwei Zhang on
thermodynamical formalism for subsystems of expanding Thurston maps, inspiring
a translation of the notion of subgroups from geometric group theory via
Sullivan's dictionary. As an application, fine large deviation properties for
expanding Thurston maps were obtained. See the preprint I here
and II here.
Xianghui has been discussing with Mario Bonk and me on formalism for the
conformal dimension, among other topics of his interests.
Ranfeng Yu has been working on the intersection between
metric geometry, probability, and dynamics. He is currently working with Tianyi
Zheng and me on quasi-isometries of percolations. Ranfeng is also talking with
Mario Bonk on this topic. On the other hand, Ranfeng is thinking about the
prevalence of periodic optimization following my work with Jian Ding and Yiwei
Zhang.
Undergraduate Students
Qiandu He has been working with me, Ilia Binder, and Yiwei
Zhang on the computability in thermodynamical formalism. A manuscript in the
uniformly expanding case, including applications to hyperbolic rational maps,
is accepted by Int. Math. Res. Not. IMRN
and available here. Qiandu has now
finished a second paper in the non-uniformly expanding case. On the other hand,
Qiandu is now working on the computability of equilibrium states in SCV under
the supervision of Fabrizio Bianchi, Michael Yampolsky, and me; as well as in smooth
dynamics with Ilia and me. Qiandu is also thinking about the computability of
maximizing measures with Yinying Huang and me.
Jie Ji studied invariant graphs on the plane under the
supervision of J. Rivera-Letelier and me. See his slides here. Jie
is now a graduate student at Stony Brook supervised by Misha Lyubich.
Xiaoran Li worked with Yiwei Zhang and me to extend
thermodynamic formalism to correspondences and Markov processes. A preprint is
available here. Xiaoran has been
working with a graduate student, Nils Hemmingsson, from Sweden, on a project on
the conformal measure for correspondences under the supervision of Misha
Lyubich and I.
Ruicen Qiu has been working with Manfred Denker, me, and Yiwei
Zhang on the study of the Martin boundary on the dynamic side of Sullivan's
dictionary. A manuscript in the uniformly expanding case is ready here.
The study in the setting of expanding Thurston maps is ongoing. Ruicen has also
been thinking about the Finite Curve Attractor Conjecture with Mario Bonk and
me.
Hanyun Zheng has been working with me on coarse expanding
conformal systems. See his slides here.
The paper available here
is accepted by Int. Math. Res. Not. IMRN. Hanyun has also been working with Pekka
Pankka and me on quasisymmetric uniformization of cellular branched covers. A
preprint is available here.
Yiqing Sun has been working on the connection (as a
dictionary) between ergodic optimization and thermodynamic formalism. The paper
available here is published in Adv. Math..
Jinru Bai has been working on geometry and Sullivan's
dictionary with Mario Bonk and me, focusing on the solenoid.
Yuke An has been working on geometry
and Sullivan's dictionary with Mario Bonk and me, focusing on the Finite
Curve Attractor Conjecture.
Zhengbo Qu has been working on the amenability of the
iterated monodromy groups for expanding Thurston maps with Tianyi Zheng and me.
Zelai Hao has been working on ergodic optimization for
the β-transformations with Yinying Huang and me. A preprint is close
to completion.
Available
projects for undergraduate students
(1)
Correspondences
and their applications in higher dimensions, with potential involvement of
Misha Lyubich.
(2)
Correspondences
and their applications in complex billiards, with potential involvement of
Misha Lyubich.
Prospective postdocs,
graduate students, and undergraduate students
There are opportunities for postdoctoral
positions, graduate study supervision, and undergraduate research projects.
Please get in touch with me via email or in person.
About Me
Miscellaneous
A Poem in Chinese (PDF)
