The (COVID-19) pandemic-induced restrictions on travel and social gatherings have prompted most conference organizers to move their events online. However, in contrast to physical conferences, virtual conferences face a challenge in efficiently scheduling talks, accounting for the availability of participants from different time-zones as well as their interests in attending different talks. In such settings, a natural objective for the conference organizers would be to maximize some global welfare measure, such as the total expected audience participation across all talks. However, we show that optimizing for global welfare could result in a schedule that is unfair to the stakeholders, i.e., the individual utilities for participants and speakers can be highly unequal. To address the fairness concerns, we formally define fairness notions for participants and speakers, and subsequently derive suitable fairness objectives for them. We show that the welfare and fairness objectives can be in conflict with each other, and there is a need to maintain a balance between these objective while caring for them simultaneously. Thus, we propose a joint optimization framework that allows conference organizers to design talk schedules that balance (i.e., allow trade-offs) between global welfare, participant fairness and the speaker fairness objectives. We show that the optimization problem can be solved using integer linear programming, and empirically evaluate the necessity and benefits of such joint optimization approach in virtual conference scheduling.