Dr. Sobol's research focus is on numerical and analytical study of dynamical systems, high performance parallel computing, and functional analysis. During his Ph.D. thesis work, Dr. Sobol developed a parallel Vlasov code for investigating collective effects in beam-beam interactions. For the numerical simulations, he has been using parallel computers at the National Energy Research Scientific Computing Center since 2003. A significant part of his dissertation work is dedicated to analytic analysis of the linearized Vlasov equation, and the corresponding integral equation of the 3rd kind. In his dissertation, he also performed some rigorous study of averaging methods for evolving distributions and extending classical averaging principles to function spaces.