Thomas Kelly
Georgia Institute of Technology, GA·Mathematics & Statistics
Graphs, networks of points joined by lines, model pairwise relationships and are basic objects in combinatorics, the mathematics of arrangements. Many classic puzzles ask about placing one structure inside another or splitting a structure into pieces.
- Fields
Mathematics & Statistics
Computer Science
- Topics
combinatorics
graph theory
hypergraphs
- Grants
- 1 known grant, through Jul 2027
What they work on
- 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.
- Prove new hypergraph decomposition results, extending classic questions on Latin squares and combinatorial designs to high-dimensional combinatorics.
- Establish 'robust' versions of embedding and decomposition results using the recently introduced notion of spreadness, and investigate statistical aspects of random combinatorial designs.
More about the research
The Knight's Tour, studied in the 9th century, and the 1800s Icosian Game both ask for a Hamilton cycle, a route that visits every point exactly once. Famous questions on Latin squares and combinatorial designs are now understood as decomposition problems for hypergraphs. In a hypergraph, a single edge can join more than two points, making it a higher-dimensional version of a graph.
Why it matters
This is basic mathematics. It aims to deepen understanding of how randomness can be used to find and split large structures in graphs and hypergraphs. It extends classic combinatorial questions, such as Hamilton cycles, Latin squares and combinatorial designs, into higher dimensions. The project names no direct applications, but the results could eventually inform other areas that use these structures.
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.
Shachar Lovett
University of California-San Diego, CA·Computer Science
Develop the theory of spreadness, a measure that no structured subset contains too many elements, into a general framework connecting existing structure-versus-randomness arguments.
Chun-Hung Liu
Texas A&M University-College Station, TX·Mathematics & Statistics·Early-career
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.
The school
Georgia Institute of Technology: 50 labs on PI Pages, $1.5B a year on research, 572 research doctorates a year.
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