Critical exponents govern the behavior of lattice models at the critical point of phase transition. In two dimensions, Schramm-Loewner evolution (SLE) is a family of random curves describing scaling limits of interfaces in lattice models and enables deriving many exponents exactly. In this talk, I will discuss the recent derivation of the backbone exponent and the mixing rate exponent by combining SLE with Liouville quantum gravity (LQG). Based on joint work with Nolin, Qian, and Sun, and with Liu and Wu.
