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Jozsef Balogh

Profile picture for Jozsef Balogh

Contact Information

Department of Mathematics
233B Illini Hall, MC-382
1409 W. Green Street
Urbana, IL 61801

Professor and J. Andrew and Susan Langan Scholar

Research Interests

graph theory, extremal combinatorics, additive combinatorics

Research Description

Balogh’s main work is the  development of the container theorem and finding several surprising applications of the method. Balogh, Morris, and Samotij published their work in the article, “Independent Sets in Hypergraphs,” in Journal of the American Mathematical Society 28 (2015). With a suitably defined notion of containment, the container theorem states that there exists a small collection of vertex subsets (containers) in an r-uniform hypergraph such that every independent set of the hypergraph is contained within a subset in the collection, with no subset in the collection inducing too many edges.  This method is an effective tool to obtain probabilistic and counting variants of several classical results in graph theory. It helped to resolve or made breakthrough of several old conjectures (among other’s Erdös’), such as counting combinatorial objects, like maximal triangle-free graphs, maximal sum-free sets; union-free sets; it has applications in Ramsey theory, discrete geometry, theoretical computer science.  The container method has become an important tool for obtaining additional results in these and other areas, there are over 40 papers using the method as one of their main tools.


PhD Mathematics, University of Memphis, 2001

Awards and Honors

NSF CAREER Award, Methods and Outreach in Modern Combinatorics" (2008–2013)
Simons Fellow (2013–2014)
Marie Curie Fellow (2013–2017)
George Pólya Prize in Combinatorics, SIAM, 2016

Additional Campus Affiliations

Professor, Mathematics

Recent Publications

Balogh, J., Garcia, R. I., Li, L., & Wagner, A. Z. (2024). Intersecting families of sets are typically trivial. Journal of Combinatorial Theory. Series B, 164, 44-67.

Balogh, J., Chen, C., McCourt, G., & Murley, C. (2024). Ramsey–Turán problems with small independence numbers. European Journal of Combinatorics, 118, Article 103872.

Araujo, I., Balogh, J., Krueger, R. A., Piga, S., & Treglown, A. (Accepted/In press). On oriented cycles in randomly perturbed digraphs. Combinatorics Probability and Computing.

Araujo, I., Balogh, J., & Luo, H. (2023). On the Maximum F5-free Subhypergraphs of a Random Hypergraph. Electronic Journal of Combinatorics, 30(4), Article P4.22.

Axenovich, M., Balogh, J., Clemen, F. C., & Weber, L. (2023). Unavoidable order-size pairs in hypergraphs — positive forcing density. Combinatorial Theory, 3(3), Article 15.

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