Konstantina-Stavroula Giannopoulou: "An approximate series solution of the semiclassical Wigner equation" The Wigner equation is a linear, non-local, kinetic evolution equation, governing the Wigner function. The Wigner function is defined as the Fourier transform of the two-point spatial correlation of the wavefunction in configuration space in classical wave propagation or as the Weyl symbol of the density operator in quantum mechanics. This function, in spite of its quantum-mechanical origin, has been proved an extremely powerful tool for the construction of high-frequency asymptotics and the homogenization of classical wavefields. The basic feature is that the integration of the Wigner function provides mean values of quantum observables or wave amplitude and energy flux of classical wave fields. In this talk, we present a new asymptotic approximation of the solution of the semiclassical Wigner equation by uniformization of WKB approximations of the Schrodinger eigenfunctions.