Yongquan Zhang 张湧权
Life during a pandemic; or, twisting along a bending lamination
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.
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
- Exotic rays and growth rate of transverse measure for measured laminations. (joint with Tina Torkaman)
[Draft available upon request]
Given any measured geodesic lamination that is not purely atomic, 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.
- Existence of an exotic plane in an acylindrical 3-manifold.
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.
- Construction of acylindrical hyperbolic 3-manifolds with quasifuchsian boundary.
Experimental Math, to appear. [preprint | journal]
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).
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.
Smale's mean value conjecture for finite Blaschke products. (joint with Tuen Wai Ng)
The Journal of Analysis 24 (2016), pp. 331--345. [arxiv | journal]
Summer research fellowship at Faculty of Science, HKU, under the supervision of Prof. Tuen Wai Ng.
- Galois groups of enumerative problems. My minor thesis.
- d-bar equations with L^2 estimates. Undergraduate final year project under the supervision of Prof. Ngaiming Mok
- Fall 2020, I am teaching Math 21a Multivariable Calculus. All instructions are online. The course homepage is here.
- Spring 2020, I taught a section of Math 21b Linear Algebra and Differential Equations before all sections moved online.
- 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.
- 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.
- 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.
The main page is here.
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.