Analysis Seminar

I will discuss the joint work with Makarov on multiple radial SLE(0) system.

We show that the traces of the multiple radial SLE(0) system are the horizontal trajectories of a class of quadratic differentials. The stationary relations establish a connection between the multiple SLE(0) systems and enumerative algebraic geometry.

Our machinery can also be applied to various multiple SLE(0) systems such as multiple radial SLE(0) with spin and multiple chordal SLE(0) with arbitrary screening charges which extend the results in \cite{ABKM20}.

From a Hamiltonian perspective, we prove that the Loewner dynamics in multiple radial SLE(0) systems are a special type of classical Calogero-Sutherland system. Furthermore, we interpret local commutation relations and $n$ quadratic null vector equations as $n$ commutating Hamiltonian flows in the phase space.

The whole theory is classical but motivated by conformal field theory.