Uploaded May 2026 | Updated September 2026, 2 weeks ago

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Conformal field theory (CFT) has proven to be a powerful framework for studying two-dimensional (2D) Bernoulli percolation at criticality. Classic applications include the derivation of certain critical exponents and crossing probabilities. Yet, the precise nature of the underlying CFT remains elusive and is a subject of active investigation in both the mathematics and physics communities. In this talk, Xin Sun will first provide an overview of this topic and then present recent progress on another fundamental planar fractal “Brownian motion,” revealing that its percolative properties may be governed by an equally rich, and perhaps more enigmatic, CFT.

For more information please visit: simonsfoundation.org/event/simons-collaboration-on-probabilistic-paths-to-quantum-field-theory-annual-meeting-2026