• Speaker(s)北京国际数学研究中心
• DateFrom 2011-07-24 To 2011-08-13
• Venue北京国际数学研究中心

暑期班从7月24日到8月13日共3周，教室在资源大厦（在北大东南门南面、太平洋和邱德拔体育馆中间那个楼）1218房间。课程有下面3个：

1．  数论在编码密码中的应用，主讲人：冯克勤（清华大学）

2．  密码函数，主讲人：李超（国防科技大学）

3．  Lectures On The Subset Sum Problem，主讲人：万大庆（University of California-Irvine）

Abstract: One of the most important and difficult problems in both mathematics and computer science is whether NP is equal to P. All the hundreds of celebrated NP-complete problems are equivalent to each other under polynomial time reduction.

In this lecture series, we will choose one of the simplest NP-complete problems, namely, the subset sum problem for an abelian group, as the starting point. We try to give a systematic study of the subset sum problem, including its algorithms, complexity and applications in coding theory,
cryptography and additive number theory.

As the subset sum problem is NP-complete, one cannot expect a satisfactory solution in general. In applications, the subset sum problem usually comes with additional structures (algebraic or combinatorial). These structured subset sums remain useful and in fact often more useful in applications! These additional structures make it possible to use mathematical tools to gain non-trivial information.

We shall give lots of examples and applications. As this is a relatively new and ongoing subject, there are plenty of opportunities for further works. We hope some of the interested students can get involved in proving some new results during the course of the summer school, and hence contribute to the development of the subject.

另外还有8个学术报告,时间安排如下: