Since 1998, the AdS/CFT correspondence conjecture becomes one of hot topics of theoretical physics. Based on this idea, physicists develop so called "holographic method" to treat some difficult problems from quantum field theory. This talk will focus on holographic condensed matter theory which is suggested by Horowitz et. al. in 2009. We will discuss following contents:
1. The basic principle and dictionary of AdS/CFT correspondence
2. The simplest holographic condensed matter model---"3H" model
3. The linearized "3H" model and related mathematical problems
4. Nonlinear "3H" model and related mathematical problems. 

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