|Location:||MSRI: Simons Auditorium, Online/Virtual|
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I will discuss certain aspects of conformal symmetry in field theory, focusing on the Liouville field on the Riemann sphere. The starting point is global formulation of conformal symmetry in terms of conformal maps of the sphere,
and the goal is to work towards "infinite-dimensional local conformal symmetry". This leads us to study the Stress-Energy Tensor, which describes how the field depends on the metric of the sphere. We will see how conformal
symmetry implies that the Stress-Energy tensor is holomorphic. However, in the presence of vertex operators, the Stress-Energy tensor becomes meromorphic, and its poles are described by the so-called Conformal Ward Identities. I will sketch how this picture can be seen in Liouville theory, and, time permitting, comment on what is the relation to the Virasoro algebra.