NSF East Asia and Pacific Summer Institute (EAPSI) for FY 2013 in Japan

Pardo John J, Rochester NY

Investigators

Abstract

This action funds John Pardo of Penn State University to conduct a research project in the Mathematical and Physical Sciences area during the summer of 2013 at the Japan Advanced Institute of Science and Technology (JAIST) in Nomi, Ishikawa Prefecture in Japan. The project title is "Classifying the Theoretical Strength of Ramsey's Theory." The host scientists are Drs. Mizuhito Ogawa and Keita Yokoyama. This project extends current research in the area of Reverse Mathematics regarding combinatorial principles and specifically Ramsey's Theory for pairs. In general, Reverse Mathematics is a program which focuses on classifying the proof-theoretic strength of mathematical theorems from all area of mathematics as subsystems of second-order arithmetic; interestingly it is the case that a large number of theorems fall into one of five major such subsystems known as "the big five", however many of the known exceptions to this are combinatorial principles - the goal is to advance what is known about Ramsey's Theory for pairs. Dr. Yokoyama has had significant success in this area before using model theoretic methods, in particular relating to approaches used in non-standard analysis, so this research begins work with these techniques in mind as well as considering proof-theoretic and recursion-theoretic methods in the work. Broader impacts of an EAPSI fellowship include providing the Fellow a first-hand research experience outside the U.S.; an introduction to the science, science policy, and scientific infrastructure of the respective location; and an orientation to the society, culture and language. These activities meet the NSF goal to educate for international collaborations early in the career of its scientists, engineers, and educators, thus ensuring a globally aware U.S. scientific workforce. Furthermore, this collaboration will strengthen the connection between mathematical researchers at Penn State and JAIST. Ideally this bond will continue to grow in the future and ultimately culminate in many additional collaborations that would have otherwise not existed.