U.S.-Czech-Hungarian Collaboration on Discrete Mathematics and Theoretical Computer Science Involving DIMACS-DIMATIA-Renyi Centers

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

This U.S.-Czech-Hungarian research project involves three teams led by Fred Roberts of Rutgers University's Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) with partners in Prague and Budapest. His counterparts are Jaroslav Nesetril of the Czech Center for Discrete Mathematics, Theoretical Informatics and Applications (DIMATIA) at Charles University and Gyula Katona of the Hungarian Academy of Sciences' Alfred Renyi Institute for Mathematics. Their collaborative research plan involves the formation of multinational "working groups" in research areas of discrete mathematics and theoretical computer science. These "working groups" will consist of a complementary mix of expertise from each center and include graduate students as well as senior and junior faculty. New members may be added as projects progress. Some participants may be drawn from other institutions, when appropriate. Additionally, smaller team collaborations resulting from working group interaction will be fostered through a visit program that allows researchers and graduate students from the partner centers to work together more intensively, with emphasis on a senior researcher in one center and a junior researcher or student at another. The topics to be studied include: 1) extremal combinatorics, 2) graph colorings and their generalizations, and 3) algebraic and geometric methods in combinatorics. Our knowledge of the interactions between algebraic geometry and combinatorics will be extended through examination of power series, hidden convexity phenomenon, and combinatorial characterizations of algebraic sets. Results should lead to advances in discrete mathematics which may be applicable to problems in group testing, communications, and statistical physics. Additionally, the involvement of outstanding junior researchers in this international network of excellence should have a significant and long-lasting influence on human resource development in all three countries. This international project linking three leading mathematics research centers fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.