  Understanding the dynamics of excitons in two dimensional semiconductors
requires a theory that incorporates the essential physics distinct from their
three-dimensional counterparts. In addition to the modified dielectric
environment, single-particle states with strongly non-parabolic dispersion
appear in many two-dimensional band structures, so that "effective mass" is
ill-defined. Focusing on electrostatically-biased bilayer graphene as an
example where quartic (and higher) dispersion terms are necessary, we present a
semi-analytic theory used to investigate the properties of ground and excited
excitonic states. This includes determination of relative oscillator strengths
and magnetic moments (g-factors) which can be directly compared to recent
experimental measurements.
