ADVANCED APPLICATIONS OF THE HYPERGRAPH CONTAINER METHOD

In collaboration with colleague Robert Morris (IMPA, Brasil) and former student Wojciech Samotij (Tel Aviv University, Israel), Professor Balogh invented the Hypergraph Container Method in 2015, resulting in more than 20 papers with various applications. In Summer 2023, several major Ramsey type results were announced in which the final key step of the proof was the container method, and recent applications of the container method include Ramsey Theory, Additive Number Theory, and Theoretical Computer Science. In January 2024, Balogh, Morris, and Samotij were awarded the Leroy P. Steele Prize for Seminal Contribution to Research by the American Mathematical Society, one of the highest awards for mathematicians.

During his release time, Professor Balogh will investigate and further develop these recent results by attending a workshop in Extremal Combinatorics at the Simons Laufer Mathematical Sciences Research Institute (MSRI) at Berkeley as well as revitalizing collaborations that were paused during the pandemic, including with Béla Bollobás (Cambridge, UK), Hong Liu (Institute of Basic Research, Seoul, Korea), Morris, and Samotij at Tel Aviv University.