It is well known that the non-intersection exponents for planar Brownian motion agree with the alternating (2N)-arm exponents for 2D percolation, both of which were originally predicted in the physics literature using conformal field theory (CFT). For 2D percolation, the CFT perspective has led to a range of exact solvability results going far beyond scaling exponents. This motivates a systematic study of planar Brownian motion from the same viewpoint.

In this talk, I will present recent progress in this direction, including several new exact formulae for Brownian partition functions in the annulus. The talk is based on joint works with Xuesong Fu, Gefei Cai and Zhuoyan Xie; with Gefei Cai, Jiaqi Liu, Wei Qian and Baojun Wu; with Guillaume Baverez, Antoine Jego and Baojun Wu; and with Gefei Cai, Baojun Wu and Zhuoyan Xie.