活动地点：

活动类型：学术报告

主讲人：王正汉

活动时间：

活动内容：

   Quantum field theories describe a variety of phenomena from the standard model in high energy physics to the fractional quantum Hall effect in 2-dimensional electron liquids in magnetic fields at almost zero temperature.
A new theme as exemplified by the topological orders in the fractional quantum Hall electron liquids is the emergent symmetries in some exotic condensed matter systems.
   Condensed matter systems consist of an enormous number of particles. While the underlying physical theories are based on local interactions such as the Coulomb interactions among electrons, elementary excitations such as
quasi-particles carrying 1/3 of the electron charge in fractional quantum Hall electron liquids are intrinsically collective behaviors of the whole systems. The emergent symmetries in such systems can be described by some tensor categories rather than the usual Lie groups.
   How to describe such quantum systems mathematically and physically is a great challenge.
   The lectures will focus on one aspect of this theme: quantum systems with (2+1)-topological quantum field theories as effective theories. Such quantum systems are called topological phases of matter (or anyonic systems, or topological orders), and potentially have great applications in quantum information science. During the month, I will start with an introduction to the topological quantum field theory. Then describe the SU(2)-Witten-Chern-Simons TQFTs, especially the unitary Jones representations of the braid groups. In the end, I will give an introduction to quantum computing and explain how to build topological quantum computers with topological phases of matter.
   There will be a companion research seminar on the classification of topological quantum field theories and applications. More information can be found on-line at: www.tqc.iu.edu <http://www.tqc.iu.edu/> or http://www.math.ucla.edu/dls/2006/wang.html