US-Hungarian Mathematics: Summer Study Program in Combinatorics, July 2011, Budapest, Hungary

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In recent decades, combinatorics has matured into a major branch of mathematics, demonstrating important connections with probability theory, number theory, geometry, computer science, and other fields. This two-week summer program in July 2011 will introduce fifteen U.S. PhD student participants to some core areas of modern combinatorics through an internationally mentored program of study at the Eötvös Loránd University, in Budapest, Hungary. The program will be led by U.S. principal investigator, Professor Bela Bollobas of the University of Memphis, in cooperation with faculty in the Department of Computer Science at Eötvös University. As a foundation for the student-centered activities, there will be four lecture series: "Random Geometric Graphs" by Professor Paul Balister of the University of Memphis, "Percolation" by Professor Bela Bollobas, "Algebraic and Geometric Methods in Additive Combinatorics" by Professor Gyula Karolyi of Eötvös University, and "Ramsey Theory" by Professor Imre Leader of the University of Cambridge. The lecturers will present fundamental and recent results as well as open problems central to advancing these topics--topics which have important applications to internet and wireless technology and offer insights into the science of neural networks. The daily schedule will consist of morning lectures and afternoon workshops. Throughout this summer program in combinatorics, the students will present papers on topics related to the courses, give informal seminars, and work in small groups. There will be ample opportunity to attend seminars given by established mathematicians. In the summer school, the junior U.S. participants will interact with international student counterparts and senior researchers, not only from Eötvös University, but also from the Alfréd Rényi Institute and the Computer and Automation Institute of the Hungarian Academy of Sciences (SZTAKI), as well as the University of Cambridge and other centers of learning in Europe. Overall, the well integrated program will promote learning in both theoretical and applied contexts. Broader impacts include an early career introduction for the U.S. PhD students to an international professional network consisting of renowned European experts in combinatorics.