Olaf Lechtenfeld (Hannover):   N=4 mechanics, WDVV equations and roots
 
N=4 superconformal $n$-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. The solutions are encoded by the finite Coxeter systems and certain deformations thereof. Nonvanishing U (and central charge) occurs only for the SU(2) and the even dihedral root systems. Thus, up to coordinate change and orthogonal composition, tunable couplings occur only in peculiar three-particle models, among which the one based on G_2+A_1 is the prime example.