Peking University, Beijing, May 5, 2009: This morning, Fields Medal winner Prof. Andrei Okounkov delivered a speech "the Most Random of All Possible Worlds" in the Yingjie Overseas Exchange center. Prof. Tian Gang, Director of Beijing International Center for Mathematical Research, Prof. Wang Changping, Dean of School of Mathematical Sciences, and Prof. Chen Dayue, Chairman of Department of Probability and Statistics of School of Mathematical Sciences, along with other teachers and students from Peking University attended the lecture. This activity was organized by Beijing International Center for Mathematical Research and hosted by Zhang Jiping, former dean of School of Mathematical Sciences.

Prof. Okounkov laid out his lecture in four aspects. He first used the example of the uniform distribution of air molecules inside a room to introduce the "Law of Large Numbers." Then he described a situation in simple random walk that as the step size in space and time are going closer to zero, the track of the simple random walk is moving closer toward a straight line. In a further effort to demonstrate that the law of large numbers will lead to a macroscopic limit shape, Prof. Okounkov used random walk on permutations (i.e. the state of process at any given time is a permutation of n objects) instead of that on numbers in the previous situation.

Lastly Prof. Okounkov introduced his recent work on “stepped surface” with Richard Kenyon. The research is a typical representation of his outstanding ability to use tools of the algebraic representation Theory to solve problems originated from the probability theory.

At the end of the lecture, Prof. Okounkov emphasized his main idea today - “the Law of Large Numbers and the characterization of limit by an optimization problem are very general and widely applicable principles.” He went on to say that while optimization problems are not always quantifiable, but the qualitative research of some of the solvable problems has given us a better view of the whole picture.

Prof. Okounkov also answered a few questions from the audience after the lecture.

Background Information: (excerpted from Wikipedia.org)

Andrei Yuryevich Okounkov is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions.

He received his doctorate at Moscow State University in 1995 under Alexander Kirillov. He has been a professor at Princeton University since 2002, and was previously an assistant professor at the University of California, Berkeley and an instructor at the University of Chicago.

In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry."

The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. The Fields Medal is often viewed as the top honor a mathematician can receive.

Founded at the behest of Canadian mathematician John Charles Fields, the medal was first awarded in 1936, to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas, and has been regularly awarded since 1950. Its purpose is to give recognition and support to younger mathematical researchers who have made major contributions.

Reported By: Seren