The ice cone family and iterated integrals for Calabi-Yau varieties

We present for the first time fully analytic results multi-loop equal-mass ice cone graphs in two dimensions. By analysing leading singularities of these integrals, we find that maximal cuts dimensions can be organised into copies same periods describe Calabi-Yau varieties banana integrals. obtain a conjectural basis master integrals at an arbitrary number loops, and solve system differential equations satisfied by terms class iterated have appeared earlier context then go on show that, when expressed canonical coordinate moduli space, our naturally written as involving geometrical invariants varieties. Our indicate how concept pure functions transcendental weight extended to case Finally, also novel representation well-known quadratic relations among reduce simple shuffle