Yongquan Zhang   张湧权

portrait

Photo credit: Zhaoyue Hu


I am a fifth-year graduate student in mathematics at Harvard University. My advisor is Curtis McMullen. Before coming to Harvard, I was a math major at Faculty of Science, The University of Hong Kong.

My email address is yqzhang (at) math.harvard.edu.

Research interests

My primary research interests include hyperbolic three-manifolds and Kleinian groups, and their connections to Teichmüller theory, hyperbolic surfaces and homogeneous dynamics. As an undergrad, I did some summer research on Smale's mean value conjecture and finite Blaschke products. I am also broadly interested in geometric function theory, several complex variables, arithmeticity, flat surfaces and moduli spaces.

Current and past projects

  1. Elementary planes in the Apollonian orbifold.
    Current work in preparation. This work attempts to address the following question: what are all the properly immersed geodesic planes in the Apollonian orbifold with elementary fundemental group, and how do they behave geometrically?

  2. Train tracks, entropy, and the halo of a measured lamination. (joint with Tina Torkaman)
    [preprint]
    Given any measured geodesic lamination that is not a multicurve, we construct uncountably many "exotic rays", i.e. geodesic rays of finite total transverse measure, not asymptotic to any leaf, nor eventually disjoint from the lamination.

  3. An exotic plane in an acylindrical 3-manifold.
    Submitted. [preprint | arxiv]
    As an application of the paper below, we show that there exists an acylindrical 3-manifold and a geodesic plane that is closed in the convex core of the manifold but not closed in the whole manifold.

  4. Construction of acylindrical hyperbolic 3-manifolds with quasifuchsian boundary.
    Exp. Math., to appear. [preprint | journal]
    In this paper, we construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold. Some animations illustrating the example can be found here. For a much shorter (and smaller in file size) excerpt focusing solely on the example see here (this is an excerpt of an earlier draft, in the current version this section is significantly simplified).

From undergrad:

  1. Generalized factorials on the image set of polynomials with integer coefficients.
    Directed Studies in Mathematics at HKU, under the supervision of Prof. Kai Man Tsang. The final report can be found here.

  2. Smale's mean value conjecture for finite Blaschke products. (joint with Tuen Wai Ng)
    J. Anal. 24 (2016), pp. 331--345. [arxiv | journal]
    Summer research fellowship at Faculty of Science, HKU, under the supervision of Prof. Tuen Wai Ng.

Expositions

  1. Galois groups of enumerative problems. My minor thesis.

  2. d-bar equations with L^2 estimates. Undergraduate final year project under the supervision of Prof. Ngaiming Mok

Teaching

  1. Fall 2020, I taught Math 21a Multivariable Calculus. All instructions took place online.

  2. Spring 2020, I taught a section of Math 21b Linear Algebra and Differential Equations before all sections moved online.

  3. Fall 2019, I was the Course Assistant for Math 212a Advanced Real Analysis taught by Prof. McMullen. The course homepage is here. I was awarded Certificate of Distinction in Teaching by the Derek Bok Center for Teaching and Learning at Harvard.

  4. Spring 2019, I held Proof Seminars for Math 22b Linear Algebra and Vector Analysis taught by Prof. Knill. The course homepage is here. I was awarded Certificate of Distinction in Teaching by the Derek Bok Center for Teaching and Learning at Harvard.

  5. Spring 2018, I taught a section of Math 21a Multivariable Calculus. I was awarded Certificate of Distinction in Teaching by the Derek Bok Center for Teaching and Learning at Harvard.

Gallery

The main page is here.

Informal seminar

Archived: Informal Geometry and Dynamics Seminar, Spring, 2020




See my webpage in Simplified Chinese (简体中文), Spanish (español). Both are, unfortunately, very outdated.