数学科学系

Department of Mathematical Sciences

2013年清华大学许宝騄讲座将举行

    2013年清华大学许宝騄讲座将于5月14日-5月16日在清华大学数学科学中心举行,美国国家科学院及美国人文与科学院院士、英国皇家学会院士、纽约大学克朗数学研究所S. R. Srinivasa Varadhan教授将访问MSC并做两场报告。S. R. Srinivasa Varadhan教授是印裔美籍数学家,他在概率论特别是建立大偏差的统一理论方面做出了重要贡献。Varadhan教授于1963年在印度统计研究所获得博士学位。Varadhan教授现任克朗数学研究所的数学教授及Frank J. Gould科学教授,他与Daniel W. Stroock关于扩散过程的研究成果以及与M. D. Donsker在大偏差方面的合作研究成果尤为出色。多年来,Varadhan教授获得过多项荣誉,其中包括由美国总统奥巴马颁发的美国国家科学奖章(2010)。他还曾获得伯克霍夫奖(1994),纽约大学的玛格丽特和赫尔曼索科尔艺术科学奖(1995),及美国数学学会颁发的Leroy P. Steele开创性研究贡献奖(1996)。2007年,Varadhan教授因其与M. D. Donsker在大偏差方面的研究成就而获得阿贝尔奖。2008年,获得政府授予的颁发的Padma Bhushan奖(印度的一个重要奖励)。Varadhan教授是美国国家科学院和美国艺术和科学院院士,同时,他还是挪威科学与文学院院士,英国皇家学院院士,第三世界科学院院士,数理统计会会士,印度科学院院士及工业与应用数学学会会士。详细信息:

Student No.: 50

Time: 16:30-17:30pm, May 14 (Tue.), May 16 (Thu.)

Instructor: S.R.Srinivasa Varadhan  [Courant Institute of Mathematical Sciences]

Place: Lecture Hall, Floor 3, Jin Chun Yuan West Building

Starting Date: 2013-5-14

Ending Date: 2013-5-16

Lecture 1

Title: Scaling Limits, Large Deviations and Particle Systems.

Time: 16:30-17:30pm, May 14 (Tue.)

Tea break: 16:00-16:30pm

Abstract: Large systems are often studied by rescaling. The limiting behavior of the rescaled system is usually simpler. The theory of large deviations which estimates the probabilities of rare events is useful in studying the collective behavior of a large system of particles and their scaling limits. We will examine some examples.  

 

Lecture 2

Title: Large Deviations and Random Graphs.

Time: 16:30-17:30pm, May 16 (Thu.)

Tea break: 16:00-16:30pm

Abstract: We consider a random graph with $N$ vertices where each edge, independently of others, has probability $p$ of being there. We can calculate easily the expected number of triangles and other subgraphs with a finite number of vertices. We examine the large deviation theory for the number of such objects and illustrate its use with some applications.