Chowla conjectured that L(1/2,\chi) never vanishes, for $\chi$ any Dirichlet character. Soundararajan showed that more than 87.5 of the values L(1/2,\chi_d), for \chi_d a quadratic character, do not vanish. Much less is known about cubic characters. Baier and Young showed that more than X^{6/7-\epsilon} of L(1/2,\chi) are non-vanishing, for \chi a primitive, cubic character of conductor of size up to X. In joint work with C. David and M. Lalin, we show that a positive proportion of these central L-values are non-vanishing in the function field setting. The same techniques can be used to prove the analogous result in the number field setting, conditional on the Generalized Riemann Hypothesis. Speaker(s): Alexandra Florea (Columbia University)