Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate
relationship between Sasakian and Kähler geometries, especially when the Kähler structure …

We describe a technique which enables one to quickly compute an infinite number of toric
geometries and their dual quiver gauge theories. The central object in this construction is …

We develop a systematic and efficient method of counting single-trace and multi-trace BPS
operators with two supercharges, for world-volume gauge theories of N D-brane probes for …

We provide a general set of rules for extracting the data defining a quiver gauge theory from
a given toric Calabi-Yau singularity. Our method combines information from the geometry …

We propose a programme for systematically counting the single and multi-trace gauge
invariant operators of a gauge theory. Key to this is the plethystic function. We expound in …

We propose a duality between quiver gauge theories and the combinatorics of dimer
models. The connection is via toric diagrams together with multiplicities associated to points …

We review recent developments in the theory of brane tilings and four‐dimensional 𝒩= 1
supersymmetric quiver gauge theories. This review consists of two parts. In part I, we …

We conjecture a general formula for assigning R-charges and multiplicities for the chiral
fields of all gauge theories living on branes at toric singularities. We check that the central …

We present the superconformal gauge theory living on the world-volume of D3 branes
probing the toric singularities with horizon the recently discovered Sasaki-Einstein manifolds …

The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories
is studied from the perspective of massless BPS geodesics. The recently constructed toric L …