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

这个美国-捷克-匈牙利研究项目涉及罗格斯大学离散数学和理论计算机科学中心（DIMACS）的Fred Roberts领导的三个团队，以及布拉格和布达佩斯的合作伙伴。 他的同行是查尔斯大学捷克离散数学、理论信息学和应用中心（DIMATIA）的Jaroslav Nesetril和匈牙利科学院阿尔弗雷德·雷尼数学研究所的Gyula Katona。 他们的合作研究计划包括在离散数学和理论计算机科学的研究领域形成多国“工作组”。这些“工作组”将由来自每个中心的专业知识互补组合组成，包括研究生以及高级和初级教师。 随着项目的进展，可能会增加新的成员。在适当情况下，还可从其他机构抽调一些参与者。 此外，将通过访问计划促进工作组互动产生的小型团队合作，该计划允许来自合作中心的研究人员和研究生更深入地合作，重点是一个中心的高级研究人员和另一个中心的初级研究人员或学生。课程内容包括：1）极值组合学，2）图着色及其推广，3）组合学中的代数和几何方法。 我们的知识代数几何和组合学之间的相互作用将通过检查幂级数，隐藏的凸性现象，和代数集的组合特征扩展。 结果应该导致离散数学的进步，这可能适用于组测试，通信和统计物理学中的问题。 此外，优秀的初级研究人员参与这一国际英才网络，将对这三个国家的人力资源开发产生重大和持久的影响。 这个国际项目连接三个领先的数学研究中心，实现了促进科学知识的计划目标，使美国和中欧的专家能够联合收割机互补人才，并在共同感兴趣和能力强的领域共享研究资源。

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.