Geometric Property (T)

One way of viewing coarse geometry is that it is the perfect tool for treating metric spaces like groups and doing representation theoretic/harmonic analytical techniques in a much larger setting. R. Willett and G. Yu define a property (T) for coarse spaces using the uniform Roe algebra. In this talk, I plan to define coarse spaces and show that the uniform Roe algebra is nice tool that acts like the group C* algebra. I will define geometric property (T) and discuss some of its properties.