We examine gender differences among the six PhD student cohorts 2004-2009 at the California Institute of Technology using a new dataset that includes information on trainees and their advisors and enables us to construct detailed measures of teams at the advisor level. We focus on the relationship between graduate student publications and: (1) their gender; (2) the gender of the advisor, (3) the gender pairing between the advisor and the student and (4) the gender composition of the team. We find that female graduate students co-author on average 8.5% fewer papers than men; that students writing with female advisors publish 7.7% more. Of particular note is that gender pairing matters: male students working with female advisors publish 10.0% more than male students working with male advisors; women students working with male advisors publish 8.5% less. There is no difference between the publishing patterns of male students working with male advisors and female students working with female advisors. The results persist and are magnified when we focus on the quality of the published articles, as measured by average Impact Factor, instead of number of articles. We find no evidence that the number of publications relates to the gender composition of the team. Although the gender effects are reasonably modest, past research on processes of positive feedback and cumulative advantage suggest that the difference will grow, not shrink, over the careers of these recent cohorts.