The International Research Fellowship Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.
This award will support a twelve month research fellowship(within a duration of 17 months) by Dr. Jozef Skokan to work with Dr. Yoshiharu Kohayakawa at the University of Sao Paulo's Instituto de Matematica de Estatistica in Sao Paulo, Brazil. Co-support for this project is provided by the Directorate of Math and Physical Sciences (MPS)'s Office of Multidisciplinary Activities (OMA).
In his dissertation research, the PI took part in a larger project aiming to develop a methodology for better understanding discrete structures called the Regularity Method. This method first decomposes a given discrete structure into substructures that are "Typical" (quasi-random) by a tool named the "Regularity Lemma" and then, in this sub-structure finds and enumerates objects of interest using a tool named "the Counting Lemma." The PI developed these two components of the Regularity Method for some special instances, more precisely the Regularity Lemma for k-uniform hypergraphs and the Counting Lemma for 4-uniform hypergraphs. The PI and host started in a related project that examined quasi-random properties of discrete structures and yielded several interesting results. They plan to focus on further developments of the Regularity Method. They are working toward a method applicable to a wider class of problems for uniform hypergraphs. They also seek a deeper understanding of the Regularity Method by exploring its applicability and limitations on several open problems.
Professor Kohayakawa is a well-established member of the mathematical community, as a member of the combinatorics group at the Instituto de Matematica e Estatistica of the University of Sao Paulo.
