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Mini-program: Renormalization Group and Applications

Mini-program: Renormalization Group and Applications
(April 15-21, 2004, USTC, 中国科技大学交叉中心水上报告厅二楼)
注:只有April 17th上午的报告在数学系三楼4703教室,其余均在交叉中心二楼。

Professor V. Rivasseau
Universite Paris XI

1) 2: 30pm-4: 00pm, April 15th
Introduction to quantum field theory, path integral & Feynman diagrams

2) 2: 30pm-4: 00pm, April 16th
Pertubation Renormalization and Renormalization group

3) 10: 30am-12: 00am, April 17th
The Jacobian Conjecture
(数学系三楼4703教室)

4) 2: 30pm-4: 00pm, April 19th
Application 1: condensed matter physics
a) the renormalization group around extended singularities;

5) 2: 30pm-4: 00pm, April 20th
b) the nature of 2-dimensional Fermi liquids

6) 2: 30pm-4: 00pm, April 21st
Application 2: renormalization in non-commutative field theory

The renormalization group (RG) relates physics at different scales. Its initial success has been in studying problems associated with divergence and running coupling constants in relativistic quantum field theory (QFT). One famous and well-accepted triumph of RG is the discovery of asymptotic freedom in non-Abelian gauge theories, which constitutes the foundation of quantum chromodynamics. In the last thirty years, the RG has found applications in many branches of physics, including critical phenomena in statistical physics, non-equilibrium systems such as turbulent fluids, and polymer physics, etc. Mathematical foundation of RG is still lacking and there are progress made by mathematical physicists.

Recently, the RG theory formulated by Wilson has been generalized to describe more general extended singularities. This new RG frontier will be presented by Prof. Rivasseau, a leading mathematical physicist in constructive QFT, emphasizing on its application to two-dimensional interacting Fermi liquids which attracted much research recently primarily due to its intimate relationship with high temperature superconductivity. To help the audiences to understand RG, a brief review on RG will be given by Prof. Rivasseau in the first two lectures.