Zhiqiang Li h1>
Beijing, China
Office
|
BICMR
78105W-1
|
Office Hours
|
By appointment
|
E-Mail
|
zli at math .pku .edu .cn
|
Positions
I got my PhD in 2015 from
UCLA under the supervision of Professor Mario Bonk.
Teaching
Conferences
& Summer Schools
International Summer School on Sullivan’s dictionary: Probability,
dynamics, and geometry (organized by Mario Bonk and Zhiqiang Li): August 26-30, 2024
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)
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)
Research Interests
My research interests lie in
the interplay of dynamical systems and geometry of spaces with fractal nature.
Publications and Preprints
Z. Li (with Ilia Binder, Qiandu He, Xianghui Shi), On computability of equilibrium states beyond uniform expansion. In preparation.
Z. Li (with Juan Rivera-Letelier), Prime orbit theorems for Collet–Eckmann maps. In preparation.
Z. Li (with Pekka Pankka and Hanyun Zheng) Bonk–Meyer theorem for
postcritically-finite uniformly quasiregular maps. In preparation.
Z. Li (with Zelai Hao, Yinying Huang), Ergodic
optimization for the β-transformations. In preparation.
Z. Li (with Yinying Huang), Ground states and periodic orbits for the Gauss map. In preparation.
Z. Li (with Ruicen Qiu), General harmonic
measures for distance-expanding dynamical systems. Available upon request.
Z. Li (with Mario Bonk and Wenbo Li), On dynamical Kapovich–Kleiner conjecture. Available upon request.
Z. Li (with Xianghui Shi), Entropy approachability and large deviation principles without
upper-semicontinuity of entropy. Available upon request.
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 Xianghui Shi), A local central limit theorem for expanding Thurston maps. Available upon request.
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. Submitted, (arXiv:2303.00514). 51 pages. (PDF)
Z. Li (with Tianyi Zheng), Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition. Submitted, minor
revision requested from Adv. Math., (arXiv: 2312.06687). 27 pages. (PDF)
Z. Li (with Tianyi Zheng), Prime orbit theorems for expanding Thurston maps: Lattès maps and split
Ruelle operators. Submitted, minor revision requested from Adv. Math., (arXiv: 2312.06688). 62 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 (with Tianyi Zheng), Prime orbit theorems for
expanding Thurston maps. Not intended for publication, (arXiv:1804.08221). 168 pages complete version
(PDF),
79 pages abridged version (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 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. 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)