, Center of Math & Theoretic Physics, NCU

**Organizers:**

Chin-Cheng Lin (National Central University)

Xiang Fang (National Central University)

Description:

Gaussian Free Fields are widely used in Conformal Field Theory by physicists since 1960s, but their mathematical theory took off only after a 2011 breakthrough by Duplantier-Sheffield, who proved a conjecture formulated by physicists. In particular, by the renowned string theorist (A.M. Polyakov) at Princeton.

In 1981, Polyakov used GFF to propose a theory of random Riemann surface, as a mathematical model for the world sheet in string theory. In 2016, Sheffield was able to define a notion of quantum length for SLE in terms of Polyakov’s framework. We seek to analyze some fine properties of this quantum length.