Jacob Fox
Stanford University, CA·Mathematics & Statistics
Any large enough system, however disorderly it looks, must contain some regular pattern. Ramsey theory and extremal combinatorics make this idea precise for discrete structures such as graphs, which are networks of points joined by lines.
- Fields
Mathematics & Statistics
Computer Science
- Topics
Ramsey theory
extremal combinatorics
graph theory
- Grants
- 1 known grant, through Jun 2027
What they work on
- 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.
- Advance the Erdős–Hajnal conjecture and its variants, which predict that graphs avoiding a fixed substructure contain unusually large cliques or independent sets.
- Pursue Alon's conjecture that every finite group has a Ramsey Cayley graph, along with related problems in additive combinatorics, information theory and random graphs, using combinatorial, probabilistic, analytic and algebraic-geometric methods.
More about the research
These fields ask how large or dense a structure must be before a given pattern is guaranteed to appear. The questions matter for their own sake. They also connect to computer science, including faster algorithms for tasks like matrix multiplication and understanding the properties of large networks.
Why it matters
This is basic mathematics. It deepens understanding of when patterns must appear in large discrete structures. According to the project, these problems relate to computer science, including the design of faster algorithms for problems such as matrix multiplication and the analysis of large networks.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
Huy Pham
California Institute of Technology, CA·Mathematics & Statistics·Early-career
Develop new toolkits for first moment obstructions, where counting expected copies of a structure rules it out, to close gaps in the theory of threshold phenomena in random discrete systems.
Bhargav Narayanan
Rutgers University-New Brunswick, NJ·Mathematics & Statistics·Early-career
Study up-sets and down-sets in the Boolean hypercube from a probabilistic viewpoint, where they encode events of interest in probabilistic combinatorics and statistical physics.
The school
Stanford University: 87 labs on PI Pages, $1.6B a year on research, 739 research doctorates a year.
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