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 Masters and Bachelors degrees from the
University of Toronto under the supervision of Professor Ilia Binder and Charles C. Pugh,
respectively.
Teaching
Conferences & Summer/Winter Schools
May 2023, 2025: Sino-Uzbeki Conference on Complex Analysis (organized by Gang
Tian, Xiaobo Liu, Zhiqiang
Li, Hanlong
Fang; Sadullaev, Abdullaev,
Eshmetov, Ibragimov, etc.)
September 2025:
International Summer School on Complex Analysis 2025
Seminars
Pacific Quasiworld
(organized by Mario Bonk, Yunping Jiang, Zhiqiang
Li, and Mitsuhiro Shishikura)
Undergraduate 3+X Complex Analysis & Complex Dynamics Seminar - Complex
Analysis, Geometry, and Dynamics (Fall 2022 - current) (PKU, organized by Zhiqiang Li)
Prof. Wens 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)
June 313 2023 Mario Bonk (UCLA)
July 1415 2023 Dylan Thurston
(Indiana University)
August 23 September 7 2023 Tianyi
Zheng (UCSD)
September 611 2023 Oliver Jenkinson
(Queen Mary, University of London)
October 918 2023 Ilia
Binder (University of Toronto)
January 614 2024 Pekka
Pankka (University of Helsinki)
March 2529 2024 Yunping
Jiang (City University of New York)
April 21May 4 2024 Daniel
Meyer (University of Liverpool)
August 2530 2024 Mario Bonk (UCLA)
August 2531 2024 John
Erik Fornζss (University of Michigan, Norwegian University of Science and
Technology)
August 2430 2024 Pekka
Pankka (University of Helsinki)
September 1519 2024 Polina Vytnova
(University of Surrey)
September 1724 2024 Mark
Pollicott (University of Warwick)
October 57 2024 LING San
(Nanyang Technological University)
December 1423 2024 Eero Saksman
(University of Helsinki)
January 1125 2025 Walter
Bergweiler (Christian-Albrechts-Universitδt zu Kiel,
Germany)
January 1125 2025 Daniel
Meyer (University of Liverpool)
January 1325 2025 Sergiy Merenkov (City
University of New York, USA)
January 1625 2025 Yunping
Jiang (City University of New York)
May 8-11 2025 DINH Tien-Cuong (National
University of Singapore)
May 8-11 2025 Fabrizio Bianchi
(University of Pisa)
May 2025 WU Guohua (Nanyang
Technological University)
September 2-13 2025 Sabyasachi
Mukherjee (Tata Institute of Fundamental Research)
September 2025 Mario Bonk (UCLA)
TBA Seonhee Lim (Seoul
National University)
Publications
and Preprints
² Z. Li (with Fabrizio Bianchi, Qiandu He, Michael Yampolsky), Computability of
equilibrium states of holomorphic endomorphisms of CP(k). In preparation.
² Z. Li
(with Mario Bonk, Wenbo Li), On dynamical
KapovichKleiner conjecture. In preparation.
² Z. Li
(with Yinying Huang,Oliver Jenkinson), Ground
states and periodic orbits for the Gauss map. In
preparation.
² Z. Li
(with Zelai Hao, Yinying
Huang, Oliver Jenkinson), Ergodic
optimization for the beta-transformations. Submitted, (arXiv:2502.12269). 46 pages. (PDF)
² Z. Li
(with Ranfeng Yu, Tianyi Zheng), Quasi-isometric
nonequivalence for random
subsets in product of trees.
² Z. Li
(with Pekka
Pankka, Hanyun
Zheng), Quasisymmetric uniformization
of cellular
branched covers. Submitted, (arXiv: 2501.00434). 81 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.
² Z. Li (with
Yiqing Sun), Tropical
thermodynamic formalism. Submitted, (arXiv:2408.10169). 49 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). 100
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), 39133985. 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: Lattθs 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), 811872.
(PDF)
² Z. Li,
Periodic points and the measure of maximal entropy of an expanding Thurston
map. Trans. Amer. Math.
Soc., 368 (2016), 89558999. (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).
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 ColletEckmann 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 has been studying invariant graphs on the
plane under the supervision of J. Rivera-Letelier and
me. See his slides here.
Xiaoran Li has been working 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. Xiaoran is also exploring another new project under the
supervision of Sabyasachi Mukherjee and me.
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 ergodic optimization.
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)