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

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. 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 University of Toronto under the supervision of Professor Ilia Binder and Charles C. Pugh, respectively.

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)

Seminars

Conformal dynamics and groups (PKU, organized by Wenyuan Yang & Zhiqiang Li)

Undergraduate Dynamics Seminar (Fall 2022 - current) (PKU, organized by Zhiqiang Li)

Prof. Wen’s seminar (PKU)

Quasiworld (UCLA)

Dynamics and Renormalization Seminar (SBU)

Undergraduate Dynamics Seminar (Spring 2022) (PKU, organized by Wenyuan Yang & Zhiqiang Li)

Undergraduate Dynamics Seminar (Fall 2020 - Spring 2021) (PKU, organized by Shaobo Gan, Disheng Xu, Zhiqiang Li)

Mini courses held locally at PKU related to our Conformal Dynamics and Groups seminar

May 17 - June 11 2023 – Kasra Rafi (University of Toronto)

June 3-13 2023 – Mario Bonk (UCLA)

TBA – Juan Rivera-Letelier (Rochester University)

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 J. Rivera-Letelier), Prime orbit theorems for Collet-Eckmann maps. In preparation (available upon request).

Z. Li (with J. Ding, Y. Zhang), On the prevalence of the periodicity of maximizing measures. Preprint, (arXiv:2303.00536). (PDF)

Z. Li (with Y. Zhang), Ground states and periodic orbits for expanding Thurston maps. Preprint, (arXiv:2303.00514). (PDF)

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Lattes maps and split Ruelle operators. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps. Preprint, (arXiv:1804.08221). Long version (PDF), short version (PDF)

Z. Li, Ergodic theory of expanding Thurston maps, volume 4 of The Atlantis Series in Dynamical Systems, Atlantis Press (Springer), 2017. (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 B. Balamohan and S. 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

Xianghui Shi has been working with me and Y. Zhang on fine large deviation properties for expanding Thurston maps, Collet-Eckmann maps, and coarse expanding conformal systems. A preprint is close to be ready, available upon request.

Yinying Huang has been working with me on the Typically Periodic Optimization Conjecture in a countable setting. A manuscript is in preparation.

Hongfei Liu has been working with me on local central limit theorems for topological Collet-Eckmann maps. A manuscript is in preparation.

Undergraduate Students

Qiandu He has been working with me, I. Binder, and Y. Zhang on the computability in thermodynamical formalism. A manuscript in the uniformly expanding case including applications to hyperbolic rational maps is available here. See his slides here.

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 me and Y. Zhang to extend the thermodynamical formalism to correspondences and Markov processes. A preprint is close to be ready, available upon request. See his slides here.

Ruicen Qiu has been working with me and Y. Zhang on the study of the Martin boundary on the dynamical 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. See his slides here.

Hanyun Zheng has been working with me on weak expansion properties and its applications in thermodynamical formalism for coarse expanding conformal systems. See his slides here.

Yiqing Sun just started working on ergodic optimization with me and Y. Zhang.

Jinru Bai just started working on large deviation at zero temperature for expanding Thurston maps.

Runjia Li just started working on amenability of the iterated monodromy groups for expanding Thurston maps with me and T. Zheng.

Baixi Liu just started working on rigidity for billiards.

Yuke An just started working on geometry and Sullivan’s dictionary.

Zhengbo Qu just started working on geometry and Sullivan’s dictionary.

Zhelai Hao

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.

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

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.

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)

Seminars

Conformal dynamics and groups (PKU, organized by Wenyuan Yang & Zhiqiang Li)

Undergraduate Dynamics Seminar (Fall 2022 - current) (PKU, organized by Zhiqiang Li)

Prof. Wen’s seminar (PKU)

Quasiworld (UCLA)

Dynamics and Renormalization Seminar (SBU)

Undergraduate Dynamics Seminar (Spring 2022) (PKU, organized by Wenyuan Yang & Zhiqiang Li)

Undergraduate Dynamics Seminar (Fall 2020 - Spring 2021) (PKU, organized by Shaobo Gan, Disheng Xu, Zhiqiang Li)

Mini courses held locally at PKU related to our Conformal Dynamics and Groups seminar

May 17 - June 11 2023 – Kasra Rafi (University of Toronto)

June 3-13 2023 – Mario Bonk (UCLA)

TBA – Juan Rivera-Letelier (Rochester University)

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 J. Rivera-Letelier), Prime orbit theorems for Collet-Eckmann maps. In preparation (available upon request).

Z. Li (with J. Ding, Y. Zhang), On the prevalence of the periodicity of maximizing measures. Preprint, (arXiv:2303.00536). (PDF)

Z. Li (with Y. Zhang), Ground states and periodic orbits for expanding Thurston maps. Preprint, (arXiv:2303.00514). (PDF)

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Lattes maps and split Ruelle operators. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds. Preprint.

Z. Li (with T. Zheng), Prime orbit theorems for expanding Thurston maps. Preprint, (arXiv:1804.08221). Long version (PDF), short version (PDF)

Z. Li, Ergodic theory of expanding Thurston maps, volume 4 of The Atlantis Series in Dynamical Systems, Atlantis Press (Springer), 2017. (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 B. Balamohan and S. 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

Xianghui Shi has been working with me and Y. Zhang on fine large deviation properties for expanding Thurston maps, Collet-Eckmann maps, and coarse expanding conformal systems. A preprint is close to be ready, available upon request.

Yinying Huang has been working with me on the Typically Periodic Optimization Conjecture in a countable setting. A manuscript is in preparation.

Hongfei Liu has been working with me on local central limit theorems for topological Collet-Eckmann maps. A manuscript is in preparation.

Undergraduate Students

Qiandu He has been working with me, I. Binder, and Y. Zhang on the computability in thermodynamical formalism. A manuscript in the uniformly expanding case including applications to hyperbolic rational maps is available here. See his slides here.

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 me and Y. Zhang to extend the thermodynamical formalism to correspondences and Markov processes. A preprint is close to be ready, available upon request. See his slides here.

Ruicen Qiu has been working with me and Y. Zhang on the study of the Martin boundary on the dynamical 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. See his slides here.

Hanyun Zheng has been working with me on weak expansion properties and its applications in thermodynamical formalism for coarse expanding conformal systems. See his slides here.

Yiqing Sun just started working on ergodic optimization with me and Y. Zhang.

Jinru Bai just started working on large deviation at zero temperature for expanding Thurston maps.

Runjia Li just started working on amenability of the iterated monodromy groups for expanding Thurston maps with me and T. Zheng.

Baixi Liu just started working on rigidity for billiards.

Yuke An just started working on geometry and Sullivan’s dictionary.

Zhengbo Qu just started working on geometry and Sullivan’s dictionary.

Zhelai Hao

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)

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