Chun-Hung Liu
Texas A&M University-College Station, TX·Mathematics & Statistics·Early-career
Graphs are networks of points joined by links. They model road systems, computer networks, molecules and social ties, and they also record the distance between any two points.
- Fields
Mathematics & Statistics
Computer Science
- Topics
structural graph theory
asymptotic dimension
graph minors
- Grants
- 1 known grant, through Jun 2027
What they work on
- Develop new structural theorems for minor-closed graph families, classes closed under deleting and contracting edges, and use them to attack embedding problems for the metric spaces these graphs support.
- Prove decomposition theorems for graph classes with polynomial expansion, a kind of sparse graph class, that avoid separator theory, the usual tool for cutting graphs into balanced parts.
- Determine where graph classes with finite asymptotic dimension, a measure of large-scale shape, fall in the hierarchy of sparse graph classes, using the new decomposition theorems.
- Extend graph minor theory from sparse to dense graphs within induced graph minor theory, drawing on notions inspired by asymptotic dimension and metric geometry.
More about the research
A long-standing question in mathematics is what large-scale shape such networks and spaces can have. Asymptotic dimension is a way of measuring that shape from far away, and it matters in metric geometry (the study of distance), in geometric group theory and in distributed computing. The PI and collaborators recently used structural graph theory to prove results about asymptotic dimension. Structural graph theory describes how complicated graphs are built from simpler pieces. This project proposes new structural theorems of this kind and aims to use them on open problems in combinatorics, theoretical computer science and geometry.
Why it matters
The project is basic mathematics. New structural theorems about graphs could resolve open questions linking combinatorics, metric geometry and theoretical computer science. They could also inform algorithmic problems such as embedding network distances into simpler spaces, and the study of sparse network classes used in computing.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jacob Fox
Stanford University, CA·Mathematics & Statistics
Determine how the number of colors and the structure of hypergraphs, networks whose edges can join more than two points, govern the off-diagonal growth of hypergraph Ramsey numbers.
Thomas Kelly
Georgia Institute of Technology, GA·Mathematics & Statistics
Use randomness and the probabilistic method to prove new results on embedding structures such as Hamilton cycles in graphs and hypergraphs, networks where an edge can join several points.
Andrew Marks
University of California-Berkeley, CA·Mathematics & Statistics
Investigate Weiss's question on whether amenability implies hyperfiniteness, meaning whether actions of orderly groups can be built from finite pieces, using Gromov's theory of asymptotic dimension, with applications to topological dynamics and operator algebras.
The school
Texas A&M University-College Station: 23 labs on PI Pages, $1.4B a year on research, 768 research doctorates a year.
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