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.
Teaching
Conferences & Summer Schools
January 20–24, 2025: International Winter School on Complex Dynamics
Seminars
Pacific Quasiworld
(organized by Mario Bonk, Yunping Jiang, Zhiqiang Li,
and Mitsuhiro Shishikura)
Conformal dynamics and groups (PKU, organized
by Zhiqiang Li, Junyi Xie, and Wenyuan Yang)
Undergraduate 3+X 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)
June 3–13 2023 Mario Bonk (UCLA)
July 14–15 2023 Dylan Thurston
(Indiana University)
August 23 – September 7 2023 Tianyi
Zheng (UCSD)
September 6–11 2023 Oliver Jenkinson
(Queen Mary, University of London)
October 9–18 2023 Ilia
Binder (University of Toronto)
January 6–14 2024 Pekka
Pankka (University of Helsinki)
March 25–29 2024 Yunping
Jiang (City University of New York)
April 21–May 4 2024 Daniel
Meyer (University of Liverpool)
August 25–30 2024 Mario Bonk (UCLA)
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)
September 15–19 2024 Polina Vytnova
(University of Surrey)
September 17–24 2024 Mark
Pollicott (University of Warwick)
Octobar 5–7 2024 LING San (Nanyang
Technological University, Singapore)
December 14–23 2024 Eero Saksman
(University of Helsinki)
Publications
and Preprints
Z. Li (with Pekka
Pankka, Hanyun Zheng),
Bonk–Meyer theorem for postcritically-finite
uniformly quasiregular maps. In preparation.
Z. Li (with Zelai Hao, Yinying
Huang, Oliver Jenkinson), Ergodic
optimization for the β-transformations. In
preparation.
Z. Li (with Yinying
Huang,Oliver
Jenkinson), Ground states and periodic orbits for the Gauss map. In
preparation.
Z. Li (with Mario Bonk, Wenbo Li), On dynamical Kapovich–Kleiner
conjecture. In preparation.
Z. Li (with Nils Hemmingsson, Xiaoran Li), Conformal measures of
(anti)holomorphic correspondences. (arXiv: 2409.01361). 37 pages. (PDF)
Z. Li
(with Ilia Binder, Qiandu He, Xianghui Shi), Computable thermodynamic formalism. Submitted.
Z. Li (with Yiqing
Sun), Tropical thermodynamic formalism. Submitted, (arXiv:2408.10169). 49 pages. (PDF)
Z. Li (with Ruicen
Qiu), General harmonic measures for distance-expanding
dynamical systems. Submitted, (arXiv:2405.02987). 44 pages. (PDF)
Z. Li (with Xianghui
Shi), Entropy density and large
deviation principles without upper semi-continuity of entropy. Submitted, (arXiv:2406.01712). 59 pages. (PDF)
Z. Li (with Xianghui
Shi), Thermodynamic formalism for
subsystems of expanding Thurston maps II. Submitted, (arXiv:2404.07247). 46 pages. (PDF)
Z. Li (with Xianghui Shi, Yiwei Zhang), Thermodynamic formalism for subsystems of expanding
Thurston maps and large deviations asymptotics. Submitted, (arXiv: 2312.15822). 57 pages. (PDF)
Z. Li (with Xiaoran
Li, Yiwei Zhang), Thermodynamic formalism for correspondences. Submitted, (arXiv: 2311.09397). 100 pages. (PDF)
Z. Li (with Hanyun
Zheng), Weak expansion
properties and a large deviation principle for coarse expanding conformal
systems. Submitted, (arXiv:2311.07305). 38 pages. (PDF)
Z. Li (with Jian Ding, Yiwei Zhang), On the prevalence of the periodicity of maximizing
measures. Adv. Math. 438, 2024, 109485. 23 pages. (PDF)
Z. Li (with Yiwei Zhang), Ground states and periodic orbits for expanding
Thurston maps. Accepted by Math. Ann., (arXiv:2303.00514). 51
pages. (PDF)
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)
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)
Z. Li (with Tianyi
Zheng), Prime orbit theorems for expanding Thurston maps: Dirichlet series and
orbifolds. Adv. Math. 443, 2024, 109600.
89 pages. (PDF)
Z. Li, Ergodic theory of expanding Thurston maps,
volume 4 of The Atlantis Series in Dynamical
Systems, Atlantis Press (Springer), 2017. 191 pages. (PDF)
Z. Li,
Weak expansion properties and large deviation principles for expanding Thurston
Maps. Adv. Math. 285 (2015), 515
–567. (PDF)
Z. Li,
Equilibrium states for expanding Thurston maps. Comm. Math. Phys.
357 (2018), 811–872. (PDF)
Z. Li,
Periodic points and the measure of maximal entropy of an expanding Thurston
map. Trans.
Amer. Math. Soc., 368 (2016), 8955–8999. (PDF)
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 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
available here. Qiandu is now thinking about new projects with Ilia Binder
and me. On the other hand, Qiandu is starting a new
project on the computability of equilibrium states in SCV under the supervision
of Fabrizio Bianchi, Michael Yampolsky, 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 weak expansion
properties and their applications in thermodynamical formalism for coarse
expanding conformal systems. See his slides here.
A preprint is available here.
Hanyun has been working with Pekka Pankka and me on building a theory of PCF uniformly
quasiregular maps. Hanyun is still thinking about CXC
systems.
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)