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

近几十年来，组合数学已发展成为数学的一个重要分支，它与概率论、数论、几何、计算机科学等领域有着重要的联系。这个为期两周的暑期项目将于2011年7月在匈牙利布达佩斯的EöTVöS洛兰德大学通过一个国际指导的学习项目向15名美国博士生学员介绍现代组合学的一些核心领域。该项目将由美国首席研究员、孟菲斯大学的贝拉·博洛巴斯教授领导，与EöTVöS大学计算机系的教职员工合作。作为以学生为中心的活动的基础，将有四个系列讲座：孟菲斯大学Paul Balister教授的《随机几何图形》，Bela Bollobas教授的《渗透》，EöTVöS大学的Gyula Karolyi教授的《加法组合学中的代数和几何方法》，以及剑桥大学Imre Leader教授的《拉姆齐理论》。讲师将介绍基本的和最新的结果，以及推动这些主题的核心开放问题--这些主题对互联网和无线技术具有重要应用，并提供对神经网络科学的见解。每天的课程表将包括上午的讲座和下午的研讨会。在整个组合数学的暑期课程中，学生们将提交与课程相关的主题的论文，进行非正式研讨会，并以小组形式进行工作。届时将有大量机会参加由知名数学家举办的研讨会。在暑期班，美国初级学员将与国际学生同行和资深研究人员进行互动，他们不仅来自EöTVöS大学，还来自匈牙利科学院阿尔弗雷德·雷尼研究所和计算机与自动化研究所，以及剑桥大学和其他欧洲学习中心。总体而言，这一整合良好的方案将促进理论和应用两方面的学习。更广泛的影响包括为美国博士生提供早期职业介绍，让他们进入由著名的欧洲组合学专家组成的国际专业网络。

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.