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In this talk I will summarise the recent progress in AdS/CFT due to the construction of the new infinite family of Sasaki-Einstein metrics Y^{p,q}, and their dual superconformal gauge theories. I will review some aspects of Sasaki-Einstein geometry and the main features of the Y^{p,q} metrics. I will then discuss the use of toric geometry to obtain a description of the corresponding Y^{p,q} Calabi-Yau singularities. I will explain how the AdS/CFT dual N=1 supersymmetric gauge theories were constructed using the combined information obtained from the metrics and the toric singularities. A crucial check on the consistency of the construction is provided by the field theory technique of a-maximisation. In the last part of the talk I will briefly discuss the recently formulated geometric dual of this, i.e. "Z-minimisation".

Edward Witten is one of the world’s preeminent string theorists. Among his many accomplishments, he is widely known for showing how five different variations of string theory all belong within a single framework. His awards range from a MacArthur \'genius grant\' to the Fields Medal - the highest honour in the world of mathematics. Professor Witten will examine key discoveries made by physicists in the 20th century such as the detection of antimatter. He will then describe how many of today’s leading scientists are working at the high energy frontier of elementary particle accelerators in their quest to uncover the quantum structures of space and time. supersymmetry, Edward Witten, particle physics, quantum mechanics, waves, Rutherford, antimatter, antiparticle, quantum uncertainty principle, accelerator, space-time