**
Amihai Hanany
**

**Tilings, Quviers & Dimers.
**

**Abstract for the series
**

When *D* branes probe a singular CY manifold the gauge theory on the
world volume of the brane gets dramatically changed. The details
depend on the nature of the singularity and in all known cases lead
to a quiver gauge theory. For toric singularities the gauge fields
and matter fields are relatively easy to compute and there exist few
equivalent methods for the computation. It has been a long standing
problem to compute the superpotential which specifies how the matter
fields couple to each other. In these lectures I will present a new
concept - dimers - and will show how they simplify and solve the
problem of computing the superpotential. Along the way we will find a
new set of integers associated with a toric diagram, denoting the
multiplicities of linear sigma model fields.
The quiver gauge theories flow in the infrared to a superconformal
fixed point, the details of it are captured using the AdS/CFT
correspondence - A dual Sasaki-Einstein manifold arises for which
some of its properties are exactly derived using the gauge theory
description.