2006 年《北京大学特别数学讲座》第九期
课 程 安 排
由我院举办的“特别数学讲座”第九期将于2006年6月中旬至7月底继续举行，讲座课程和主讲教授基本信息如下：
1. 课程名称：A Basic Introduction to Geometric Measure Theory
Abstract: In many problems in PDEs and calculus of variations, low dimensional sets in Euclidean spaces arise naturally. Well known examples include singular sets of minimal surfaces and harmonic maps. Geometric measure theory is developed to treat those sets. The course is divided into three parts. In the first part, we introduce the Hausdorff measure, which measures the size of low dimensional sets. In the second part, we discuss area and coarea formulas, which are important in the calculation in the measure of those sets. In the final part, we discuss countably rectifiable sets, which are the basic object in geometric measure theory. Usually, it is the starting point for a fine regularity. Prerequisite knowledge is kept to a minimum. We only assume some basic knowledge of measures and integrations.
主讲教授：Prof. Han Qing（Notre Dame University，USA）
授课时间：June 12 – June 30
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2. 课程名称：Subfactors and its applications
Abstract: I will lecture on the basics of subfactor theory invented by Vaughan Jones and describe some of its applications.
主讲教授：Prof. Xu Feng (University of California at Riverside, USA)
授课时间：July 3 – July 28
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3. 课程名称：Mathematical aspects of general relativity
Abstract:
主讲教授：1. Prof. Qing Jie (UCSC, USA)
2. Prof. P. T. Chrusciel (University of Tours, France)
授课时间：June 20 – July 15
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4. 课程名称：Khovanov Knot Homology
Abstract: We will introduce the construction of Khovanov knot homology in
this course. The highlight of this combinatorial construction is to give a proof of Milnor's conjecture about the slice genus of torus knots, which was proved previously using gauge theoretical techniques.
主讲教授：Prof. Lin Xiaosong (University of California at Riverside, USA)
授课时间：July 3- July 14
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5.课程名称：Integer valued invariants in real enumerative geometry
Abstract: I will explain how to extract from classical problems of real enumerative geometry some integer valued invariants. As in the theory of Gromov-Witten invariants, these invariants are in fact attached to the underlying real symplectic manifold
and only depend on its deformation class. The problems that will be discussed will concern real symplectic four-manifolds even though similar phenomenons apppear in any dimension. They will actually mostly concern the number of real rational planar curves of degree d which pass through 3d-1 points, or the number of
real planar conics tangent to five given real planar conics.
The course will be organized around the following talks:
1,2) Examples of problems of real enumerative geometry and the associated invariants of real symplectic four-manifolds.
3) Moduli space of real rational pseudo-holomorphic curves of a real symplectic four-manifold.
4) Critical points and Gromov's compactness theorem.
5,6) Proofs of the main results.
主讲教授：Prof. Y.-V. Welschinger (ENS Lyon, France)
授课时间：July 3 -July 15
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除上述课程外，田刚教授等还将组织一些专题讨论班，另有一些教授短期来访做学术报告，欢迎参加。
1、数学特讲办地址：北京大学理科楼群一号楼1282E（邮编100871），
电话：010-62759534，E-mail: 1282@math.pku.edu.cn。
2、报名时间：4月1日至5月10日(申请表格可从网上下载，非北大生源的同志报名时请寄回由导师推荐信和所在单位加盖公章的申请表，同时在线登记，并用E-mail发送一份，以便核查)
3、报名时请写清楚您的详细地址、E-MAIL以及联系电话。
4、各课程的讲课时间可能还会有调整，请及时注意通知。
5、包括各课程内容摘要等在内有关信息可以到网上查询了解,
http://www.math.pku.edu.cn:8000/misc/jiangzuo/jinagzuo.htm
北京大学数学科学学院
北京大学数学研究所
北京大学数学及其应用重点实验室