Hezunwu

Sep 2014 – Jun 2019, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Fundamental Mathematics, Ph.D. (Combined Master's-Ph.D. program)

Sep 2010 – Jun 2014, Wuhan University, Mathematics Base Class , Bachelor's Degree

My current research primarily focuses on circle packing and related fields, spectral geometry on graphs , and geometric group theory.

Circle Packing and Related Fields

Circle packing originally refers to configurations of circles in the plane where the interiors of the circles are disjoint and at most tangent to each other. This concept admits many generalizations.
It was introduced as a crucial tool by the renowned mathematician and Fields Medalist Thurston in his famous work on the geometrization of 3-manifolds, leading to the well-known Koebe–Andreev–Thurston Theorem. This field lies at the intersection of combinatorics, geometry, and analysis, and remains highly active.

I am mainly interested in the metrics induced by circle packing on surfaces (or sphere packing in 3-manifolds), particularly the existence and uniqueness of such metrics with respect to certain geometric quantities. This area offers many research topics, and much can be learned through hands-on exploration. I warmly welcome interested students to participate.

Spectral Geometry

The famous mathematician Kac once gave a well-known lecture titled Can One Hear the Shape of a Drum?
It addresses whether one can identify a geometric object (such as a bounded domain in Euclidean space) from the eigenvalues of its Laplacian operator. This is a classic example of spectral geometry, which has long been a thriving and active branch of mathematics.

My main interest lies in estimating the upper and lower bounds of Steklov/Laplacian eigenvalues on graphs and manifolds—since eigenvalues are often not computable exactly—and their relationships with geometric quantities (such as boundary volume, domain volume, etc.), especially for negatively curved objects.
There are also related topics currently under investigation. Much can be explored through learning by doing, and I sincerely welcome interested students to join.

Geometric Group Theory

Geometric group theory became an independent mathematical discipline following the work of the Wolf Prize-winning mathematician Gromov in the 1980s.
It connects the combinatorial and algebraic properties of groups with the topological and geometric properties of the spaces on which they act. It is closely related to low-dimensional topology and geometry, group theory, differential geometry, and other fields, and remains an active area of research.

I am primarily interested in its intersection with the two areas mentioned above. Currently, there are also related research topics available. Much can be learned through active participation, and I warmly welcome interested students to take part.

Probability Theory and Mathematical Statistics；
Linear Algebra and Analytic Geometry；
Fundamentals of Calculus；
Medical Advanced Mathematics；
Mathematical Analysis III.