SUPERSTRING PERTURBATION THEORY AT TWO-LOOPS
                         Duong H. Phong

Abstract:
  In string perturbation theory, Feynman rules correspond to a measure on the moduli space of Riemann surfaces, whose moments are the string scattering amplitudes. This measure has been difficult to determine, due to a geometric difficulty, which is the occurrence of "supermoduli" at higher loop orders. Recently, this difficulty has been overcome at 2-loops, which is the lowest order where supermoduli arise. This talk is devoted to a survey of recent progresses and open problems in this direction, including models with broken supersymmetry, global corrections to the BRST formalism, two-dimensional superholomorphicity and holomorphicity, and string-induced corrections to the Einstein-Hilbert action.