报告题目：The master field on the plane

报告人：Thierry Levy (巴黎六大)

时间：2013年3月21日（星期四）16:00-17:00

地点：理科楼数学科学系A304会议室

摘要：The Yang-Mills field on the plane is a collection of random matrices indexed by the set of loops based at the origin on the plane. These matrices belong to a fixed compact group, for example the unitary group U(N), and the Yang-Mills field can be thought of as a random unitary representation of the group of rectifiable loops on the plane, the group operation being concatenation. I will describe the large N limit of this random reprensentation, in particular the fact that it converges almost surely towards a deterministic limit. This limit, which is an instance of what physicists call the master field, takes the form of a plain deterministic real-valued function on the set of loops. This function can be computed by a recursive algorithm based on the so-called Makeenko-Migdal equations, which are a graphical translation of the algebraic structure of freeness.

报告人简介：Thierry Levy教授，现任法国巴黎六大教授，曾在法国CNRS（Strasbourg）和巴黎高师任职。主要研究领域包括Yang-Mills测度，随机过程、随机场，紧Lie群中的热核问题等。

联系人：叶俊