Lizhi Chen

Currently I work in the mathematics department at Lanzhou University.

Before that, I was a post-doctoral fellow at Chern Institute of Mathematics of Nankai University.

I did my doctoral studies at Department of Mathematics of Oklahoma State University.

This page will be updated regularly. I also update my homepage by using Github pages and Wordpress pages , for the purpose of convenience of internet access (sometimes I may have no access for one of these three sites).

Address: School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China.

Email: lizhi.chen.math@gmail.com (lizhi dot chen dot math at gmail dot com) lizhi.chen@outlook.com (lizhi dot chen at outlook dot com)

Research

Research Interests: Low dimensional geometry and topology, Hyperbolic geometry, Quantitative geometry and quantitative topology, Systolic geometry and asymptotic geometry, Differential geometry.

List of Papers:

Edward Bryden and Lizhi Chen, Stability for a class of three-tori with small negative scalar curvature, (2024), submitted, current version: 05/14/2024. arXiv:2404.12795, download: PDF file.
Lizhi Chen, Counting manifolds with bounded asymptotic invariants, (2021), preprint, current version: October 16, 2024, download: PDF file.
Lizhi Chen, Triangulation complexity and systolic volume of hyperbolic manifolds, (2021), [arXiv] , preprint, current version: 11/29/2021, download: [PDF] file, (8 pages).
Lizhi Chen, Gromov's systolic inequality via smoothing technique, (2021), Proceedings of the International Young Seminars on Bounded Cohomology and Simplicial Volume, Chapter 4, to appear in: London Mathematical Society Lecture Notes Series, an online version is available at Link .
Lizhi Chen, Embolic volume and finite domination, (2019), current version: 05/03/2021, download : PDF file.
Lizhi Chen, Covering trick and embolic volume, (2019), submitted, current version: 05/03/2021. PDF file.
Lizhi Chen and Weiping Li, Systoles of surfaces and 3-manifolds, (2015), Geometry and Topology of Submanifolds and Currents, 61 -- 80, Contemp. Math., 646, Amer. Math. Soc., Providence, RI, 2015.
Lizhi Chen, Systolic freedom of 3-manifolds, (2014), Thesis (Ph.D.), Oklahoma State University.

Talks:

Topological complexity of hyperbolic manifolds represented by using systolic geometry, January 18 -- 21, 2022, The 17th East Asian Conference on Geometric Topology , January 18 -- 21, 2022.
Topological complexity of closed manifolds with nonzero simplicial volume, November 25, 2021, Geometry and Topology Seminar, Sichuan University.
Homology and homotopy complexity via systolic geometry, 38th Annual Workshop in Geometric Topology (online), June 15 -- 17, 2021, Texas Christian University.
Homology and homotopy complexity via systolic geometry, Seminar at Beijing International Center for Mathematical Research (online), May 12, 2021, Peking University.
Gromov's systolic inequality via smoothing technique, International young seminar on bounded cohomology and simplicial volume (online), November 23, 2020.
Covering theorem and embolic volume of compact manifolds, Conference on Algebraic Topology and Applied Topology, January 3--8, 2020, Chongqing University of Technology.
Covering theorem and embolic volume of compact manifolds, Geometry and Topology Seminar, December 30, 2019, Capital Normal University.
Berger's embolic inequality and topology, 2019 Southwest Geometry Workshop, December 13 -- 15, 2019, Sichuan University.

Seminar Organizing: Geometry and Topology Seminar

Talks in this seminar are conducted in person (with hybrid options) or online, as indicated.

Teaching

Spring 2025:

Teaching Courses:

Mathematical Writing and Academic English, (graduate course).
Honors Undergraduate Topology.
Undergraduate Topology.
Topics in Geometry and Topology: Geometry of Surfaces (undergraduate advanced topic course).

Spring 2024:

Teaching Courses:

Algebraic Topology, (graduate course).
Mathematical Writing and Academic English, (graduate course).
Undergraduate Topology.
Honors Undergraduate Topology.

Spring 2023:

Teaching Courses:

Mathematical Writing and Academic English, (graduate course).
Undergraduate Topology.
Undergraduate Topology for Cuiying Honors College.

Spring 2022:

Teaching Courses:

Mathematical writing and academic English, (graduate course).
Undergraduate Topology (in Chinese).
Undergraduate Topology for Cuiying Honors College (in Chinese).

Undergraduate Thesis Advised:

Yunjie Wang, Self intersection numbers of closed geodesic on hyperbolic surfaces.
Ni An, Invariants of hyperbolic knots.
Changyi Guan, Hyperbolic surfaces with systoles that fill.
Fan Wu, Geometry and topology of arithmetic hyperbolic surfaces.
Fengyin Wu, Benjamini-Schramm convergences of hyperbolic surfaces.

Fall 2021:

I have no teaching courses in the classroom this semester.
Undergraduate reading project (online):

Teichmuller space

We totally have three undergraduate students and one master student in this group. Main reference is: Benson Farb and Dan Margalit, A primer on mapping class groups , Princeton University Press, 2012. Our plan is to cover "Part 2" of Farb and Margalit's book.

Spring 2021:

Undergraduate Topology (in Chinese).
Algebraic Topology (a graduate course for master students).

Past Courses:

Undergraduate Topology, Spring 2017, Spring 2019, Spring 2020 , Spring 2021 (at Lanzhou University).
Algebraic Topology (graduate course), Spring 2018, Spring 2019, Spring 2020, Spring 2021 (at Lanzhou University).
College Calculus (in Chinese), Spring 2018, Spring 2017 (at Lanzhou University).
Calculus for Medical School (in Chinese), Fall 2016 (at Lanzhou University).
Precalculus ( Discussion Session ), Fall 2013, Fall 2012, Fall 2011, Fall 2010, Fall 2009 (at Oklahoma State University).
Calculus II, Summer 2013 (at Oklahoma State University).
Calculus I, Spring 2013, Spring 2012 (at Oklahoma State University).
Elementary Calculus, Summer 2012, Summer 2010 (at Oklahoma State University).
Calculus III, Summer 2011 (at Oklahoma State University).
Elementary Calculus (Discussion Session), Spring 2011, Spring 2010, Spring 2009 (at Oklahoma State University).

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