Zhiqiang Li

中文版 Chinese version


Assistant Professor
Beijing International Center for Mathematical Research (BICMR), Peking University

School of Mathematical Sciences (SMS), Peking University

Beijing, China

 

Office

BICMR 78105W-1

Office Hours

By appointment

E-Mail

zli at math .pku .edu .cn


Research Interests

My research interests lie in the interplay of dynamical systems and geometry of spaces with fractal nature.

Positions

I am currently holding an Assistant Professor position jointly at Beijing International Center for Mathematical Research (BICMR) and the School of Mathematical Sciences (SMS) at Peking University.

I got my PhD in 2015 from UCLA under the supervision of Professor Mario Bonk.

Teaching

Fall 2020: Higher Mathematics A (I)

Spring 2021: Higher Mathematics A (II)

Fall 2021: Higher Mathematics A (I)

Spring 2022: Functions of One Complex Variable

Fall 2022: Higher Mathematics A (I)

Spring 2023: Topic Course on Dynamical Systems (taught in English)

Spring 2024: Functions of One Complex Variable

Conferences & Summer Schools

August 26-30, 2024: International Summer School on Sullivan’s dictionary: Probability, dynamics, and geometry (organized by Mario Bonk and Zhiqiang Li)

January 13-17, 2025: Conference on Holomorphic Dynamics and Fractal Geometry (organized by Junyi Xie and Zhiqiang Li)

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)

Quasiworld (UCLA)

Prof. Wen s seminar (PKU)

Dynamics and Renormalization Seminar (SBU)

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 2024 Juan Rivera-Letelier (Rochester University)

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), BonkMeyer 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 Ruicen Qiu), General harmonic measures for distance-expanding dynamical systems. Submitted, (arXiv:2405.02987). 44 pages. (PDF).

Z. Li (with Mario Bonk and Wenbo Li), On dynamical Kapovich–Kleiner conjecture. Available upon request.

Z. Li (with Xianghui Shi), Entropy density 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 Ilia Binder, Qiandu He, Yiwei Zhang), On computability of equilibrium states. Submitted, (arXiv: 2311.09374). 41 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. To appear in Adv. Math. 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 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 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

My Curriculum Vitae

My Research Statement

Miscellaneous

A Poem in Chinese (PDF)