Title: Von Neumann equivalence rigidity Abstract: The notion of measure equivalence of discrete groups has been introduced by Gromov as a measurable variant of the topological notion of quasi-isometry. Measure equivalence of groups is tightly related to the theory of II_1 factors: if G and H are measure equivalent, then they admit free ergodic probability measure preserving action for which their von Neumann algebras are stably isomorphic. Also, two groups G and H are called W*-equivalent if...

Title: Zero mode issue in the minus-minus component calculation of the transition form factors in the light-front dynamics. Abstract: Among the three forms of Hamiltonian dynamics Dirac proposed in 1949, the light-front dynamics (LFD) has the most kinematical Poincare operators. In particular, the longitudinal boost operator becomes kinematical in the LFD. The LFD has very distinct vacuum properties, leading to its zero-mode issue which complicates calculations. The minus components in the LFD...