Overburdened White Men (and Women)

New percolation crossing formulas and second-order modular forms

“…PK is grateful to Don Zagier for leading us to Proposition 2.2, for other useful conversations, and for his kind hospitality at the Collège de France, where part of this research was done. He also thanks C. Hongler for an advance copy of [17] and J. J. H. Simmons and R. M. Ziff for useful conversations.…”

“…Their integrals give Π h , Π hv , and N h , where the latter is the expected number of horizontally crossing clusters. (This was calculated first via conformal field theory [5,6] and later rigorously [17]. )…”