# Conformal symmetry in physics

Symmetry has arguably been the principal guiding notion in the development of theoretical physics. In this colloquium I will give a brief overview of some of the consequences of symmetry in physics before presenting some examples of conformal symmetry.

In two dimensions conformal symmetry gives rise to an infinite set of independent constraints that a conformally symmetric physical system would have to satisfy. These constraints make exact solutions of certain conformally invariant quantum field theories possible; have important applications in the thermodynamics of many body physics, particle physics and string theory; and have a beautiful mathematical structure.